{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Chapter 4 – Training Linear Models**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_This notebook contains all the sample code and solutions to the exercises in chapter 4._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's make sure this notebook works well in both python 2 and 3, import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# To support both python 2 and python 3\n",
    "from __future__ import division, print_function, unicode_literals\n",
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "np.random.seed(42)\n",
    "\n",
    "# To plot pretty figures\n",
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "\n",
    "# Where to save the figures\n",
    "PROJECT_ROOT_DIR = \".\"\n",
    "CHAPTER_ID = \"training_linear_models\"\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True):\n",
    "    path = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID, fig_id + \".png\")\n",
    "    print(\"Saving figure\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format='png', dpi=300)\n",
    "\n",
    "# Ignore useless warnings (see SciPy issue #5998)\n",
    "import warnings\n",
    "warnings.filterwarnings(action=\"ignore\", module=\"scipy\", message=\"^internal gelsd\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear regression using the Normal Equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "X = 2 * np.random.rand(100, 1)\n",
    "y = 4 + 3 * X + np.random.randn(100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure generated_data_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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R9r82Wlld7PbWytB0QG0BjgRuBx4GPgX8RlMrn/TRd5Nf9GEVWVMBPBgQw9bbZoiUWuGOsv813covsdtRmtNoQGXmo8Bbej+tqKviHKwEm/6iD6vI3vOedrq/Sup2K73CXWz/a7qVP+3d3uo278W3BMMqwaa/6PNVZG0+ZK+Eiq3rFW7TYT9t3d6aLlMXUE107wyrBJv+opfUailJE/8Pk97Hmgx79yOVLDIbHUg3tpmZmZydnR1p3qa6d+Zbz1IqrlLPlwzqSjlhsmUtvQtRalNE3JKZM3Utb6paUE1178x31Dnuke+oQdd2OHStUp5kC6TrXYhSl0xVQDXZzVZHJTissoMnX1N0/vnthsNSKuW2Q3VSPGcjNWeqAqrk/vRhFfawym4wDD796faP2MetlLvW4hpHyfuYNG06HVDDKv1Sbgk0uK5hFfZ8lV1/GJx+Otx4Y7tH7ONWytPeDVbKiEVp2nU2oJZzlF7CNUvzBeqwMDj++PaP2MeplCfxIMG2P7+k5nU2oJZzlF7KNUvzGRZa85WvxMq7P2SPOGJ5d++e5u5CSQvrbEAt5yh9Wq5ZKrnynivHKI/mKOnWP5LK0dmAWk6lP+xv27r4cjnrLb3yXqx8owSso+aklauzAQWjnReZLwDm/r19O9x6K7z1rfDoo7BmzfIq+nECZ7ktoNIr78XKN0rAOmpOWrk6HVCLWSgA+qdBVUlC9fqaa5o5X7LcFlDplfdi5Rs1YB01J61MnQiopXaDLRQA/dMi6innuIFTRwuo9Mp7ofKVHrCS2lV8QD344NK7wRYKgP5pq1ZBJjz2WPXeWWctraxLGa230ivo0gNWUnuKv1nss541kzt3zrJvXxUkW7ZUzz2as1jraqHp/dOgnqAocdi3JDWh7pvFFh9Qxx47k3ffPbvoeaTShllL0kpTd0AdUNeCJuXgg6vg2bLlyQE0381W1awdO2Dr1uq3JNWl+HNQMP95itKHWa8EtmIlTUonAmo+DjJoX+kXC0vqrlYCKiJ+HLgV+IPMfN1yluUosHbZipU0KW21oD4KfKWlddduJY/csxUraVIaD6iIOAP4HvAl4MeaXn/dPAdjK1bSZDQ6ii8iDgPeB7xjkfk2RcRsRMzu2rWrmcItUZsjCR09J2maNd2C2gJcnpnfiQXuL5SZ24BtADMzM0VfqNXWORhbbpKmXWMBFREnAKcCL2pqnU1o6xyMo+ckTbsmW1AbgQ3At3utp0OAVRHx/Mz8yQbLUbs2zsE4ek7StGsyoLYBn+x7/atUgfXmBsswNRw9J2naNRZQmfkD4AdzryNiD/BwZpY9CqJgjp6TNM1au5NEZm5ua92jWsnXN0lS2zp9q6NRLDVkHCUnSe2a6oBaTsg4Sk6S2lX84zaWYzkX0c6Nklu1qp5Rcl5UK0njmeoW1HKGYtc5Ss7uQkka31QH1HJDpq5RcnYXStL4pjqgoIyh2F5UK0njm/qAKoEX1UrS+AyohpTQkpOkLpnqUXySpO4yoCRJRTKgJElFMqAkSUUyoCRJRTKgJElFMqAkSUUyoCRJRTKgJElFMqAkSUUyoCRJRWosoCLioIi4PCLujojdEfE3EXFaU+uXJHVLky2o1cD/BV4K/AhwAfCpiNjQYBkkSR3R2N3MM/NBYHPfW38cEXcC/wK4q6lySJK6obVzUBFxFHAMcNuQaZsiYjYiZnft2tV84SRJrWsloCJiDfAx4OrM/Obg9MzclpkzmTmzbt265gsoSWpd4wEVEQcA1wKPAOc2vX5JUjc0+kTdiAjgcuAo4Gcz89Em1y9J6o6mH/n+O8CxwKmZ+VDD65YkdUiT10EdDbwJOAHYGRF7ej9nNlUGSVJ3NDnM/G4gmlqfJKnbvNWRJKlIBpQkqUgGlCSpSAaUJKlIBpQkqUgGlCSpSAaUJKlIBpQkqUgGlCSpSAaUJKlIBpQkqUgGlCSpSAaUJKlIBpQkqUgGlCSpSAaUJKlIBpQkqUgGlCSpSAaUJKlIBpQkqUiNBlREHB4RfxgRD0bE3RHxy02uX5LUHasbXt9HgUeAo4ATgP8VEV/NzNsaLockqXCNtaAi4mDgdODCzNyTmX8J/BHw+qbKIEnqjiZbUMcAj2Xm7X3vfRV46eCMEbEJ2NR7uTcivt5A+ep2JHBv24UYUxfLDN0sdxfLDN0sdxfLDN0s93PrXFiTAXUI8MDAe98HDh2cMTO3AdsAImI2M2cmX7x6dbHcXSwzdLPcXSwzdLPcXSwzdLPcETFb5/KaHCSxBzhs4L3DgN0NlkGS1BFNBtTtwOqI+PG+934CcICEJOlJGguozHwQuA54X0QcHBEnAa8Erl3kT7dNvHCT0cVyd7HM0M1yd7HM0M1yd7HM0M1y11rmyMw6l7fwyiIOB64AXgbcB7w7Mz/eWAEkSZ3RaEBJkjQqb3UkSSqSASVJKlIrATXqPfmi8v6IuK/38/6IiL7pJ0TELRHxg97vEwoo8zsj4usRsTsi7oyIdw5MvysiHoqIPb2fP51Umccs9+aIeLSvXHsi4tl900vc1jcMlPeRiLi1b3pj2zoizo2I2YjYGxFXLTLv2yNiZ0Q8EBFXRMRBfdM2RMRf9LbzNyPi1EmVeZxyR8TZvf/3ByLiOxHxgYhY3Td9e0Q83Letv1VAmc+JiH0D+8jGvumlbuvLBsq8NyJ2901vclsfFBGX976HuyPibyLitAXmr3ffzszGf4BPAL9HdfHuT1FdsHvckPneBHwLeBbwTOAbwK/0ph0I3A28HTgIOK/3+sCWy/xrwE9SXQT93F6ZzuibfhdwaoHbejPwu/Mso8htPeTvtgMXtbGtgVcDrwJ+B7hqgfleDvwjcBzwtF6Z/1Pf9B3Ah4CnUN0a7HvAugLK/Wbg5N6+8EzgFqpBTv3b/o2FbetzgL9cYHqR23rI310FXNHStj64VzdsoGrQ/DzVtasbhsxb+7498Q84zwd+BDim771r+z9I3/tfAjb1vf53wM29f/8M8Pf0Bnr03vs28Io2yzzkb38L+O2+101WmuNs683MH1DFb+veF2hf/xenyW3dt85LFqk0Pw78Zt/rU4CdvX8fA+wFDu2bfiO9g7I2yz1k/ncAn+l73VilOca2Pod5Aqor27r3fdgNvLTNbT1Qpq8Bpw95v/Z9u40uvvnuyXfckHmP600bNt9xwNey90l7vjbPcpZrnDL/UEQE1VHn4MXIH4uIXRHxpxHxE/UWdT/jlvsXIuK7EXFbRLy57/3itzVwFnBjZt418H5T23pUw/bpoyLiiN60OzJz98D0SWzn5XoJT96vt0bEvRFxU39XWste1CvT7RFxYV+3ZFe29enALuCLA++3sq0j4iiq7+iwGyzUvm+3EVAj35OvN+/3B+Y7pFfxD05baDnLNU6Z+22m2sZX9r13JtXR/tHAXwB/EhFPraWUTzZOuT8FHAusA/49cFFEvLZvOaVv67OoukL6NbmtRzVsn4bq8zW5nZcsIt4AzAAf7Hv7XcCzqbr/tgGfiYjntFC8fl8EXgA8naqify0wd064E9saOBu4ZuDgsJVtHRFrgI8BV2fmN4fMUvu+3UZAjXNPvsF5DwP29P6zmry339jriohzqSrNn8vMvXPvZ+ZNmflQZv4gM7dS9cOePIEywxjlzsxvZOY9mbkvM78E/BfgF8ddTg2Wsq1/CvinwB/0v9/wth7VsH0aqs9X/P0qI+JVwFbgtMz84Z22M/OvMnN3Zu7NzKuBm4CfbaucvTLdkZl3ZubjmXkr8D7a2aeXJCLWAxuBa/rfb2NbR8QBVF3tjwDnzjNb7ft2GwE1zj35butNGzbfbcALe62pOS+cZznLNdZ9BHtHmO8GTsnM7yyy7ARikXmWajn3P+wvV7Hbuuds4LrM3LPIsie5rUc1bJ/+x8y8rzft2RFx6MD0Iu5XGRGvAP478Au9Cn8hJWzrQYP7dLHbuuf1wE2Zecci8010W/e+95dTPWj29Mx8dJ5Z69+3WzrJ9kmqkVoHAycx/8iyXwH+lqop+896H2ZwFN/bqEaWnctkR5aNWuYzgZ3AsUOmre/97YHAWqruhl3AEQVs61dSjbwJ4MVUgyLOLnlb9+Z9Sm/6T7e5ralGba6lal1c2/v36iHzvaK3fzwfeCrwBfYf6XQzVdfZWuDfMPmRZaOW+6epbk/2kiHTnko1gmttb3lnAg/SN9ClpTKfBhzV+/fzgK8DF5e+rfvm/xbwhja3dW+dl/W21SGLzFf7vj2RDzTCBz4cuL63Yb8N/HLv/ZOpuvDm5gvgA8B3ez8fYP+RZC+iGu76EPDXwIsKKPOdwKNUTdq5n8t6046jGlzwYO/L/nlgppBt/YlemfYA3wTOG1hOcdu6995rqcIyBt5vdFtTnW/MgZ/NVEG5B1jfN+87qIbjPkB1fvKgvmkbqEZpPURVQU10FOKo5aY6h/fYwH59Q2/aOuArVN0136OqiF5WQJk/2NvODwJ3UHXxrSl9W/fmPbFX7kMHltH0tj66V86HB/7vz2xi3/ZefJKkInmrI0lSkQwoSVKRDChJUpEMKElSkQwoSVKRDChJUpEMKElSkQwoSVKRDChJUpEMKGkCIuIpvUejf7v/sde9af+j9yjyM9oqn9QFBpQ0AZn5EHAx8KPAW+bej4itVE+GfmtmfrKl4kmd4L34pAmJiFVUTw19OtUD5t4IfJjqjtrva7NsUhcYUNIERcTPA5+hevTAvwYuzczz2i2V1A0GlDRhEfHXVI8r+STVo0NyYPq/Bc4DTgDuzcwNjRdSKpDnoKQJiohf4omnjO4eDKee+4FLgV9vrGBSB9iCkiYkIn6GqnvvM1QPsXwNcHxm/u08878K+IgtKKliC0qagIj4l8B1wE1UTx+9AHic6nHfkkZgQEk1i4jnA58FbgdelZl7M/PvgMuBV0bESa0WUOoIA0qqUUSsB/6E6rzSaZn5QN/kLcBDwAfaKJvUNavbLoA0TTLz21QX5w6bdg/wT5otkdRdBpTUst4FvWt6PxERa4HMzL3tlkxqlwElte/1wJV9rx8C7gY2tFIaqRAOM5ckFclBEpKkIhlQkqQiGVCSpCIZUJKkIhlQkqQiGVCSpCIZUJKkIv1/zuSC65hhRY0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108e55d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "save_fig(\"generated_data_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_b = np.c_[np.ones((100, 1)), X]  # add x0 = 1 to each instance\n",
    "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new = np.array([[0], [2]])\n",
    "X_new_b = np.c_[np.ones((2, 1)), X_new]  # add x0 = 1 to each instance\n",
    "y_predict = X_new_b.dot(theta_best)\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10acc06d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_predict, \"r-\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.axis([0, 2, 0, 15])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure in the book actually corresponds to the following code, with a legend and axis labels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure linear_model_predictions\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10acca6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_predict, \"r-\", linewidth=2, label=\"Predictions\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "save_fig(\"linear_model_predictions\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.21509616]), array([[2.77011339]]))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.predict(X_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `LinearRegression` class is based on the `scipy.linalg.lstsq()` function (the name stands for \"least squares\"), which you could call directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best_svd, residuals, rank, s = np.linalg.lstsq(X_b, y, rcond=1e-6)\n",
    "theta_best_svd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function computes $\\mathbf{X}^+\\mathbf{y}$, where $\\mathbf{X}^{+}$ is the _pseudoinverse_ of $\\mathbf{X}$ (specifically the Moore-Penrose inverse). You can use `np.linalg.pinv()` to compute the pseudoinverse directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.pinv(X_b).dot(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: the first releases of the book implied that the `LinearRegression` class was based on the Normal Equation. This was an error, my apologies: as explained above, it is based on the pseudoinverse, which ultimately relies on the SVD matrix decomposition of $\\mathbf{X}$ (see chapter 8 for details about the SVD decomposition). Its time complexity is $O(n^2)$ and it works even when $m < n$ or when some features are linear combinations of other features (in these cases, $\\mathbf{X}^T \\mathbf{X}$ is not invertible so the Normal Equation fails), see [issue #184](https://github.com/ageron/handson-ml/issues/184) for more details. However, this does not change the rest of the description of the `LinearRegression` class, in particular, it is based on an analytical solution, it does not scale well with the number of features, it scales linearly with the number of instances, all the data must fit in memory, it does not require feature scaling and the order of the instances in the training set does not matter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear regression using batch gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "eta = 0.1\n",
    "n_iterations = 1000\n",
    "m = 100\n",
    "theta = np.random.randn(2,1)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n",
    "    theta = theta - eta * gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new_b.dot(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_bgd = []\n",
    "\n",
    "def plot_gradient_descent(theta, eta, theta_path=None):\n",
    "    m = len(X_b)\n",
    "    plt.plot(X, y, \"b.\")\n",
    "    n_iterations = 1000\n",
    "    for iteration in range(n_iterations):\n",
    "        if iteration < 10:\n",
    "            y_predict = X_new_b.dot(theta)\n",
    "            style = \"b-\" if iteration > 0 else \"r--\"\n",
    "            plt.plot(X_new, y_predict, style)\n",
    "        gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n",
    "        theta = theta - eta * gradients\n",
    "        if theta_path is not None:\n",
    "            theta_path.append(theta)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    plt.axis([0, 2, 0, 15])\n",
    "    plt.title(r\"$\\eta = {}$\".format(eta), fontsize=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure gradient_descent_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c208358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.subplot(131); plot_gradient_descent(theta, eta=0.02)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(132); plot_gradient_descent(theta, eta=0.1, theta_path=theta_path_bgd)\n",
    "plt.subplot(133); plot_gradient_descent(theta, eta=0.5)\n",
    "\n",
    "save_fig(\"gradient_descent_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stochastic Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_sgd = []\n",
    "m = len(X_b)\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure sgd_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e7a9eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_epochs = 50\n",
    "t0, t1 = 5, 50  # learning schedule hyperparameters\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    for i in range(m):\n",
    "        if epoch == 0 and i < 20:                    # not shown in the book\n",
    "            y_predict = X_new_b.dot(theta)           # not shown\n",
    "            style = \"b-\" if i > 0 else \"r--\"         # not shown\n",
    "            plt.plot(X_new, y_predict, style)        # not shown\n",
    "        random_index = np.random.randint(m)\n",
    "        xi = X_b[random_index:random_index+1]\n",
    "        yi = y[random_index:random_index+1]\n",
    "        gradients = 2 * xi.T.dot(xi.dot(theta) - yi)\n",
    "        eta = learning_schedule(epoch * m + i)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_sgd.append(theta)                 # not shown\n",
    "\n",
    "plt.plot(X, y, \"b.\")                                 # not shown\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)                     # not shown\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)           # not shown\n",
    "plt.axis([0, 2, 0, 15])                              # not shown\n",
    "save_fig(\"sgd_plot\")                                 # not shown\n",
    "plt.show()                                           # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21076011],\n",
       "       [2.74856079]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SGDRegressor(alpha=0.0001, average=False, epsilon=0.1, eta0=0.1,\n",
       "       fit_intercept=True, l1_ratio=0.15, learning_rate='invscaling',\n",
       "       loss='squared_loss', max_iter=50, n_iter=None, penalty=None,\n",
       "       power_t=0.25, random_state=42, shuffle=True, tol=None, verbose=0,\n",
       "       warm_start=False)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDRegressor\n",
    "sgd_reg = SGDRegressor(max_iter=50, penalty=None, eta0=0.1, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.16782089]), array([2.72603052]))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg.intercept_, sgd_reg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mini-batch gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_mgd = []\n",
    "\n",
    "n_iterations = 50\n",
    "minibatch_size = 20\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "t0, t1 = 200, 1000\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "t = 0\n",
    "for epoch in range(n_iterations):\n",
    "    shuffled_indices = np.random.permutation(m)\n",
    "    X_b_shuffled = X_b[shuffled_indices]\n",
    "    y_shuffled = y[shuffled_indices]\n",
    "    for i in range(0, m, minibatch_size):\n",
    "        t += 1\n",
    "        xi = X_b_shuffled[i:i+minibatch_size]\n",
    "        yi = y_shuffled[i:i+minibatch_size]\n",
    "        gradients = 2/minibatch_size * xi.T.dot(xi.dot(theta) - yi)\n",
    "        eta = learning_schedule(t)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_mgd.append(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.25214635],\n",
       "       [2.7896408 ]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_bgd = np.array(theta_path_bgd)\n",
    "theta_path_sgd = np.array(theta_path_sgd)\n",
    "theta_path_mgd = np.array(theta_path_mgd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure gradient_descent_paths_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bd3b0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7,4))\n",
    "plt.plot(theta_path_sgd[:, 0], theta_path_sgd[:, 1], \"r-s\", linewidth=1, label=\"Stochastic\")\n",
    "plt.plot(theta_path_mgd[:, 0], theta_path_mgd[:, 1], \"g-+\", linewidth=2, label=\"Mini-batch\")\n",
    "plt.plot(theta_path_bgd[:, 0], theta_path_bgd[:, 1], \"b-o\", linewidth=3, label=\"Batch\")\n",
    "plt.legend(loc=\"upper left\", fontsize=16)\n",
    "plt.xlabel(r\"$\\theta_0$\", fontsize=20)\n",
    "plt.ylabel(r\"$\\theta_1$   \", fontsize=20, rotation=0)\n",
    "plt.axis([2.5, 4.5, 2.3, 3.9])\n",
    "save_fig(\"gradient_descent_paths_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.random as rnd\n",
    "\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 0.5 * X**2 + X + 2 + np.random.randn(m, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure quadratic_data_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fbf50b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"quadratic_data_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
    "X_poly = poly_features.fit_transform(X)\n",
    "X[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929,  0.56664654])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_poly[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.78134581]), array([[0.93366893, 0.56456263]]))"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X_poly, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure quadratic_predictions_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fe26dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new=np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "X_new_poly = poly_features.transform(X_new)\n",
    "y_new = lin_reg.predict(X_new_poly)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"quadratic_predictions_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure high_degree_polynomials_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ff06208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "for style, width, degree in ((\"g-\", 1, 300), (\"b--\", 2, 2), (\"r-+\", 2, 1)):\n",
    "    polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n",
    "    std_scaler = StandardScaler()\n",
    "    lin_reg = LinearRegression()\n",
    "    polynomial_regression = Pipeline([\n",
    "            (\"poly_features\", polybig_features),\n",
    "            (\"std_scaler\", std_scaler),\n",
    "            (\"lin_reg\", lin_reg),\n",
    "        ])\n",
    "    polynomial_regression.fit(X, y)\n",
    "    y_newbig = polynomial_regression.predict(X_new)\n",
    "    plt.plot(X_new, y_newbig, style, label=str(degree), linewidth=width)\n",
    "\n",
    "plt.plot(X, y, \"b.\", linewidth=3)\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"high_degree_polynomials_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "def plot_learning_curves(model, X, y):\n",
    "    X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=10)\n",
    "    train_errors, val_errors = [], []\n",
    "    for m in range(1, len(X_train)):\n",
    "        model.fit(X_train[:m], y_train[:m])\n",
    "        y_train_predict = model.predict(X_train[:m])\n",
    "        y_val_predict = model.predict(X_val)\n",
    "        train_errors.append(mean_squared_error(y_train[:m], y_train_predict))\n",
    "        val_errors.append(mean_squared_error(y_val, y_val_predict))\n",
    "\n",
    "    plt.plot(np.sqrt(train_errors), \"r-+\", linewidth=2, label=\"train\")\n",
    "    plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"val\")\n",
    "    plt.legend(loc=\"upper right\", fontsize=14)   # not shown in the book\n",
    "    plt.xlabel(\"Training set size\", fontsize=14) # not shown\n",
    "    plt.ylabel(\"RMSE\", fontsize=14)              # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure underfitting_learning_curves_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fbc9b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "plot_learning_curves(lin_reg, X, y)\n",
    "plt.axis([0, 80, 0, 3])                         # not shown in the book\n",
    "save_fig(\"underfitting_learning_curves_plot\")   # not shown\n",
    "plt.show()                                      # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure learning_curves_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fbb86a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "polynomial_regression = Pipeline([\n",
    "        (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
    "        (\"lin_reg\", LinearRegression()),\n",
    "    ])\n",
    "\n",
    "plot_learning_curves(polynomial_regression, X, y)\n",
    "plt.axis([0, 80, 0, 3])           # not shown\n",
    "save_fig(\"learning_curves_plot\")  # not shown\n",
    "plt.show()                        # not shown"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regularized models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure ridge_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108e55cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "np.random.seed(42)\n",
    "m = 20\n",
    "X = 3 * np.random.rand(m, 1)\n",
    "y = 1 + 0.5 * X + np.random.randn(m, 1) / 1.5\n",
    "X_new = np.linspace(0, 3, 100).reshape(100, 1)\n",
    "\n",
    "def plot_model(model_class, polynomial, alphas, **model_kargs):\n",
    "    for alpha, style in zip(alphas, (\"b-\", \"g--\", \"r:\")):\n",
    "        model = model_class(alpha, **model_kargs) if alpha > 0 else LinearRegression()\n",
    "        if polynomial:\n",
    "            model = Pipeline([\n",
    "                    (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
    "                    (\"std_scaler\", StandardScaler()),\n",
    "                    (\"regul_reg\", model),\n",
    "                ])\n",
    "        model.fit(X, y)\n",
    "        y_new_regul = model.predict(X_new)\n",
    "        lw = 2 if alpha > 0 else 1\n",
    "        plt.plot(X_new, y_new_regul, style, linewidth=lw, label=r\"$\\alpha = {}$\".format(alpha))\n",
    "    plt.plot(X, y, \"b.\", linewidth=3)\n",
    "    plt.legend(loc=\"upper left\", fontsize=15)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    plt.axis([0, 3, 0, 4])\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.subplot(121)\n",
    "plot_model(Ridge, polynomial=False, alphas=(0, 10, 100), random_state=42)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(122)\n",
    "plot_model(Ridge, polynomial=True, alphas=(0, 10**-5, 1), random_state=42)\n",
    "\n",
    "save_fig(\"ridge_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.55071465]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "ridge_reg = Ridge(alpha=1, solver=\"cholesky\", random_state=42)\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.13500145])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg = SGDRegressor(max_iter=5, penalty=\"l2\", random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())\n",
    "sgd_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.5507201]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge_reg = Ridge(alpha=1, solver=\"sag\", random_state=42)\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure lasso_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ff0eb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.subplot(121)\n",
    "plot_model(Lasso, polynomial=False, alphas=(0, 0.1, 1), random_state=42)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(122)\n",
    "plot_model(Lasso, polynomial=True, alphas=(0, 10**-7, 1), tol=1, random_state=42)\n",
    "\n",
    "save_fig(\"lasso_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.53788174])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "lasso_reg = Lasso(alpha=0.1)\n",
    "lasso_reg.fit(X, y)\n",
    "lasso_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.54333232])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import ElasticNet\n",
    "elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5, random_state=42)\n",
    "elastic_net.fit(X, y)\n",
    "elastic_net.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure early_stopping_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ff16e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 2 + X + 0.5 * X**2 + np.random.randn(m, 1)\n",
    "\n",
    "X_train, X_val, y_train, y_val = train_test_split(X[:50], y[:50].ravel(), test_size=0.5, random_state=10)\n",
    "\n",
    "poly_scaler = Pipeline([\n",
    "        (\"poly_features\", PolynomialFeatures(degree=90, include_bias=False)),\n",
    "        (\"std_scaler\", StandardScaler()),\n",
    "    ])\n",
    "\n",
    "X_train_poly_scaled = poly_scaler.fit_transform(X_train)\n",
    "X_val_poly_scaled = poly_scaler.transform(X_val)\n",
    "\n",
    "sgd_reg = SGDRegressor(max_iter=1,\n",
    "                       penalty=None,\n",
    "                       eta0=0.0005,\n",
    "                       warm_start=True,\n",
    "                       learning_rate=\"constant\",\n",
    "                       random_state=42)\n",
    "\n",
    "n_epochs = 500\n",
    "train_errors, val_errors = [], []\n",
    "for epoch in range(n_epochs):\n",
    "    sgd_reg.fit(X_train_poly_scaled, y_train)\n",
    "    y_train_predict = sgd_reg.predict(X_train_poly_scaled)\n",
    "    y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
    "    train_errors.append(mean_squared_error(y_train, y_train_predict))\n",
    "    val_errors.append(mean_squared_error(y_val, y_val_predict))\n",
    "\n",
    "best_epoch = np.argmin(val_errors)\n",
    "best_val_rmse = np.sqrt(val_errors[best_epoch])\n",
    "\n",
    "plt.annotate('Best model',\n",
    "             xy=(best_epoch, best_val_rmse),\n",
    "             xytext=(best_epoch, best_val_rmse + 1),\n",
    "             ha=\"center\",\n",
    "             arrowprops=dict(facecolor='black', shrink=0.05),\n",
    "             fontsize=16,\n",
    "            )\n",
    "\n",
    "best_val_rmse -= 0.03  # just to make the graph look better\n",
    "plt.plot([0, n_epochs], [best_val_rmse, best_val_rmse], \"k:\", linewidth=2)\n",
    "plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"Validation set\")\n",
    "plt.plot(np.sqrt(train_errors), \"r--\", linewidth=2, label=\"Training set\")\n",
    "plt.legend(loc=\"upper right\", fontsize=14)\n",
    "plt.xlabel(\"Epoch\", fontsize=14)\n",
    "plt.ylabel(\"RMSE\", fontsize=14)\n",
    "save_fig(\"early_stopping_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.base import clone\n",
    "sgd_reg = SGDRegressor(max_iter=1, warm_start=True, penalty=None,\n",
    "                       learning_rate=\"constant\", eta0=0.0005, random_state=42)\n",
    "\n",
    "minimum_val_error = float(\"inf\")\n",
    "best_epoch = None\n",
    "best_model = None\n",
    "for epoch in range(1000):\n",
    "    sgd_reg.fit(X_train_poly_scaled, y_train)  # continues where it left off\n",
    "    y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
    "    val_error = mean_squared_error(y_val, y_val_predict)\n",
    "    if val_error < minimum_val_error:\n",
    "        minimum_val_error = val_error\n",
    "        best_epoch = epoch\n",
    "        best_model = clone(sgd_reg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(239, SGDRegressor(alpha=0.0001, average=False, epsilon=0.1, eta0=0.0005,\n",
       "        fit_intercept=True, l1_ratio=0.15, learning_rate='constant',\n",
       "        loss='squared_loss', max_iter=1, n_iter=None, penalty=None,\n",
       "        power_t=0.25, random_state=42, shuffle=True, tol=None, verbose=0,\n",
       "        warm_start=True))"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_epoch, best_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "t1a, t1b, t2a, t2b = -1, 3, -1.5, 1.5\n",
    "\n",
    "# ignoring bias term\n",
    "t1s = np.linspace(t1a, t1b, 500)\n",
    "t2s = np.linspace(t2a, t2b, 500)\n",
    "t1, t2 = np.meshgrid(t1s, t2s)\n",
    "T = np.c_[t1.ravel(), t2.ravel()]\n",
    "Xr = np.array([[-1, 1], [-0.3, -1], [1, 0.1]])\n",
    "yr = 2 * Xr[:, :1] + 0.5 * Xr[:, 1:]\n",
    "\n",
    "J = (1/len(Xr) * np.sum((T.dot(Xr.T) - yr.T)**2, axis=1)).reshape(t1.shape)\n",
    "\n",
    "N1 = np.linalg.norm(T, ord=1, axis=1).reshape(t1.shape)\n",
    "N2 = np.linalg.norm(T, ord=2, axis=1).reshape(t1.shape)\n",
    "\n",
    "t_min_idx = np.unravel_index(np.argmin(J), J.shape)\n",
    "t1_min, t2_min = t1[t_min_idx], t2[t_min_idx]\n",
    "\n",
    "t_init = np.array([[0.25], [-1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure lasso_vs_ridge_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c1fb630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def bgd_path(theta, X, y, l1, l2, core = 1, eta = 0.1, n_iterations = 50):\n",
    "    path = [theta]\n",
    "    for iteration in range(n_iterations):\n",
    "        gradients = core * 2/len(X) * X.T.dot(X.dot(theta) - y) + l1 * np.sign(theta) + 2 * l2 * theta\n",
    "\n",
    "        theta = theta - eta * gradients\n",
    "        path.append(theta)\n",
    "    return np.array(path)\n",
    "\n",
    "plt.figure(figsize=(12, 8))\n",
    "for i, N, l1, l2, title in ((0, N1, 0.5, 0, \"Lasso\"), (1, N2, 0,  0.1, \"Ridge\")):\n",
    "    JR = J + l1 * N1 + l2 * N2**2\n",
    "    \n",
    "    tr_min_idx = np.unravel_index(np.argmin(JR), JR.shape)\n",
    "    t1r_min, t2r_min = t1[tr_min_idx], t2[tr_min_idx]\n",
    "\n",
    "    levelsJ=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(J) - np.min(J)) + np.min(J)\n",
    "    levelsJR=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(JR) - np.min(JR)) + np.min(JR)\n",
    "    levelsN=np.linspace(0, np.max(N), 10)\n",
    "    \n",
    "    path_J = bgd_path(t_init, Xr, yr, l1=0, l2=0)\n",
    "    path_JR = bgd_path(t_init, Xr, yr, l1, l2)\n",
    "    path_N = bgd_path(t_init, Xr, yr, np.sign(l1)/3, np.sign(l2), core=0)\n",
    "\n",
    "    plt.subplot(221 + i * 2)\n",
    "    plt.grid(True)\n",
    "    plt.axhline(y=0, color='k')\n",
    "    plt.axvline(x=0, color='k')\n",
    "    plt.contourf(t1, t2, J, levels=levelsJ, alpha=0.9)\n",
    "    plt.contour(t1, t2, N, levels=levelsN)\n",
    "    plt.plot(path_J[:, 0], path_J[:, 1], \"w-o\")\n",
    "    plt.plot(path_N[:, 0], path_N[:, 1], \"y-^\")\n",
    "    plt.plot(t1_min, t2_min, \"rs\")\n",
    "    plt.title(r\"$\\ell_{}$ penalty\".format(i + 1), fontsize=16)\n",
    "    plt.axis([t1a, t1b, t2a, t2b])\n",
    "    if i == 1:\n",
    "        plt.xlabel(r\"$\\theta_1$\", fontsize=20)\n",
    "    plt.ylabel(r\"$\\theta_2$\", fontsize=20, rotation=0)\n",
    "\n",
    "    plt.subplot(222 + i * 2)\n",
    "    plt.grid(True)\n",
    "    plt.axhline(y=0, color='k')\n",
    "    plt.axvline(x=0, color='k')\n",
    "    plt.contourf(t1, t2, JR, levels=levelsJR, alpha=0.9)\n",
    "    plt.plot(path_JR[:, 0], path_JR[:, 1], \"w-o\")\n",
    "    plt.plot(t1r_min, t2r_min, \"rs\")\n",
    "    plt.title(title, fontsize=16)\n",
    "    plt.axis([t1a, t1b, t2a, t2b])\n",
    "    if i == 1:\n",
    "        plt.xlabel(r\"$\\theta_1$\", fontsize=20)\n",
    "\n",
    "save_fig(\"lasso_vs_ridge_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_function_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e7aadd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(-10, 10, 100)\n",
    "sig = 1 / (1 + np.exp(-t))\n",
    "plt.figure(figsize=(9, 3))\n",
    "plt.plot([-10, 10], [0, 0], \"k-\")\n",
    "plt.plot([-10, 10], [0.5, 0.5], \"k:\")\n",
    "plt.plot([-10, 10], [1, 1], \"k:\")\n",
    "plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n",
    "plt.plot(t, sig, \"b-\", linewidth=2, label=r\"$\\sigma(t) = \\frac{1}{1 + e^{-t}}$\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.legend(loc=\"upper left\", fontsize=20)\n",
    "plt.axis([-10, 10, -0.1, 1.1])\n",
    "save_fig(\"logistic_function_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['data', 'target', 'target_names', 'DESCR', 'feature_names']"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "iris = datasets.load_iris()\n",
    "list(iris.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iris Plants Database\n",
      "====================\n",
      "\n",
      "Notes\n",
      "-----\n",
      "Data Set Characteristics:\n",
      "    :Number of Instances: 150 (50 in each of three classes)\n",
      "    :Number of Attributes: 4 numeric, predictive attributes and the class\n",
      "    :Attribute Information:\n",
      "        - sepal length in cm\n",
      "        - sepal width in cm\n",
      "        - petal length in cm\n",
      "        - petal width in cm\n",
      "        - class:\n",
      "                - Iris-Setosa\n",
      "                - Iris-Versicolour\n",
      "                - Iris-Virginica\n",
      "    :Summary Statistics:\n",
      "\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "                    Min  Max   Mean    SD   Class Correlation\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "    sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
      "    sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
      "    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
      "    petal width:    0.1  2.5   1.20  0.76     0.9565  (high!)\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "    :Class Distribution: 33.3% for each of 3 classes.\n",
      "    :Creator: R.A. Fisher\n",
      "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      "    :Date: July, 1988\n",
      "\n",
      "This is a copy of UCI ML iris datasets.\n",
      "http://archive.ics.uci.edu/ml/datasets/Iris\n",
      "\n",
      "The famous Iris database, first used by Sir R.A Fisher\n",
      "\n",
      "This is perhaps the best known database to be found in the\n",
      "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
      "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
      "data set contains 3 classes of 50 instances each, where each class refers to a\n",
      "type of iris plant.  One class is linearly separable from the other 2; the\n",
      "latter are NOT linearly separable from each other.\n",
      "\n",
      "References\n",
      "----------\n",
      "   - Fisher,R.A. \"The use of multiple measurements in taxonomic problems\"\n",
      "     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
      "     Mathematical Statistics\" (John Wiley, NY, 1950).\n",
      "   - Duda,R.O., & Hart,P.E. (1973) Pattern Classification and Scene Analysis.\n",
      "     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
      "   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
      "     Structure and Classification Rule for Recognition in Partially Exposed\n",
      "     Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
      "     Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
      "   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
      "     on Information Theory, May 1972, 431-433.\n",
      "   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
      "     conceptual clustering system finds 3 classes in the data.\n",
      "   - Many, many more ...\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(iris.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris[\"data\"][:, 3:]  # petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int)  # 1 if Iris-Virginica, else 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
       "          penalty='l2', random_state=42, solver='liblinear', tol=0.0001,\n",
       "          verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "log_reg = LogisticRegression(random_state=42)\n",
    "log_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10fc0a5c0>]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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VrdFbKV+kPIvvXUz9MvWz/0blNXQgrPIoo0fDJ59Amzbw229Op/F9+0/vp+1nbdkavZWbS93M6odWa5H3QVrolUf5v/+DVq3g4EFo2xY2bXI6ke/ac2oP7Sa3Iyo2ilvK3cKqh1ZRpXgVp2OpXKCFXnmU4sXturSdO0NMDNx2m50gTbnXrhO7aDe5HQfOHKBlxZYsvW8ppQvr4DhfpYVeeZzgYJg/H3r3hjNnbNHXYu8+26K38ZfJf+FI3BHaVWnH4nsXUyyomNOxVC7SQq88UsGCMGMG9Olji/277zqdyDdsOraJ2ybfRnRCNB2rd2TRoEW6nms+oAPalMcKDLRP0d56Kzz+uNNpvN+26G10/KIjJ8+f5M5ad/L1PV8TFBDkdCyVB/SKXnm0wEB47jkISq9HFy7ozJfXY9eJXXT4osOlIj/nnjla5PMRLfTKayQmQkQEtG4NGzc6ncZ77Dm1hw5fdLjUXfP1PV9TMKCg07FUHtJCr7yGn59di/biDdpdu5xO5Pn2n97P7V/cfunG67z+8/RKPh/SQq+8RmCgXXu2Sxc4ccKuXLVvn9OpPNfhs4e5/YvbLw2hXDhgIYUDCzsdSzlAC73yKgULwpw59mGqw4dtsT961OlUnufkuZN0+rITUbFRhJcP19E1+ZwWeuV1CheGBQugaVPYswc6dYJTp5xO5TkSkhK4a9pd7Dyxk/pl6us4eaWFXnmnYsVg8WIIC4OqVW3fvYKk1CQiZkWw9vBaqhSrwuJ7F1OyUEmnYymH6Th65bVKl4Yff4QSJWz/fX6XZtJ4cN6DLN6zmNKFS/P94O8pX6S807GUB9AreuXVypTJKPIXLsC4cWCMs5mcYIzhqcVPMW3rNEIKhLBo0CJql6rtdCzlIfSKXvkEY+zcOIsW2Zu0r7/udKK89a9V/+L9te9TwL8Ac/vNJbx8uNORlAfRK3rlE0RgxAi7HOEbb9gr+/zi802f88KyFxCEKb2m0KF6B6cjKQ+jhV75jDvvhAkT7NcjRsDcuc7myQvL9y5n6IKhAHx4x4f0rdfX4UTKE2mhVz7loYfgtdcgLQ0GDIDVq51OlHt2xOyg18xeJKcl81SLp3is2WNOR1IeSgu98jmjRsEjj9ibsz16wN69Tidyv+Pxx7lr2l2cSTxDrzq9+HfnfzsdSXkwvRmrfI4IfPSRXY6wSBG46SanE7nXueRz3D39bvad3kezCs2Y0nsKfqLXbOrqtNArnxQQAF99Zac39vOhGpialsqgOYNYd2QdVYtXZX7/+Tp/jcqWD/0TUOpKhQtnFPmEBPj0U+8fY//skmeZu2suxYOK8+3AbykbUtbpSMoL6BW98nlpaXbGy59+gvh4GDnS6UTX59MNn/Luz+8S6BfInHvmEBYa5nQk5SX0il75PD8/O9wS4KmnYOFCZ/Ncj1UHVjH8m+EAjO82nvbV2jucSHkTLfQqX+jfH1591Xbd9O8Pmzc7nch1+0/vp/fM3iSnJTOy+UgeavKQ05GUl9FCr/KNl16CQYNsf32PHnbxEk8XnxRP9xndiTkXQ5caXXQYpbouWuhVviFib8jeeivs3w/33APJyU6nuro0k8Z9kfex5fgWapeqzYw+Mwjw09tqKue00Kt8JSgIIiPt2PqKFSE11elEVzf6x9FE7oqkWMFizO8/n+JBxZ2OpLyUXh6ofKdCBfj1VyhXzl7le6JZ22cxZsUY/MSPmX1mcnPpm52OpLyYXtGrfKl8+YwiHxcH27c7m+dym45t4oG5DwDwdqe36VKzi7OBlNdzqdCLSEkRiRSRBBHZLyIDr9G2qYisEJF4ETkuIk+4L65S7nX0KLRsadedPXLE6TQQez6WiFkRnE85z4ONH2RkCy8d9K88iqtX9B8BSUBZYBAwTkTqZW4kIqWB74BPgFJATeB790RVyv1Kl7bb0aN24ZILF5zLkmbSuH/u/UTFRtG0XFM+vutjxFP7lpRXybbQi0gwEAG8ZIyJN8asAuYDg7No/hSw2Bgz1RiTaIyJM8bsdG9kpdwnMBBmz4bKlWHtWhg+3LlpEt5c9SYLdi+gRFAJvur7FUEBQc4EUT7HlSv62kCKMWb3Zfs2A3+6ogdaAKdEZLWIRIvIAhGp7I6gSuWW0FCYNw8KFYLPPoPx4/M+w7K9yxi1fBQAU3pPoVqJankfQvksVwp9CHA2074zQJEs2lYE7geeACoDe4HpWX2oiDwiIutFZH1MTIzriZXKBY0bw8SJ9usnnrBX93nl8NnD9P+qP2kmjVFtR3FnrTvz7oerfMGVQh8PFM20rygQl0Xb80CkMWadMeYC8CrQSkSKZW5ojJlgjAk3xoSHhobmNLdSbjdgAPztb/YhqrxahjApNYm+s/sScy6GjtU7Mvq20Xnzg1W+4so4+t1AgIjUMsb8nr6vEZDVgLQtwOU9nF4+KazKb95+G267zd6YzQvPLXmONYfWULFoRab1noa/n3/e/GCVr2R7RW+MSQDmAK+JSLCItAZ6AF9m0fwzoJeINBaRQOAlYJUx5ow7QyuVWwoUuLLI5+YUCTO3zeT9te8T6BfI7L6zCQ3W32xV7nB1eOVwoBAQje1zH2aM2S4ibUUk/mIjY8wy4AXgm/S2NYGrjrlXypPt3AmNGtkpE9z+2TE7eXjBwwCM7TKWFhVbuP+HKJXOpSkQjDGngJ5Z7F+JvVl7+b5xwDi3pFPKQd99Z4v9/fdDvXpQu7Z7Pjc+KZ6IWRHEJ8UzoP4AHrv1Mfd8sFJXoVMgKHUVI0dCnz52ioTeve30xjfKGMPQBUPZeWIndUPrMuHuCfpQlMp1WuiVugoRmDQJ6tSxc+EMHXrjD1P955f/MGPbDEIKhPD1PV8TUiAk+29S6gZpoVfqGooUgTlzICQEpk+HDz+8/s9ac3ANT33/FACTuk+iTuk6bkqp1LVpoVcqG2Fh9soe4Omn4fffr90+KzEJMfSd3ZeUtBRGNh9J33p93RtSqWvQ+eiVckHfvvDCC1CzJtSqlbPvTU1LZcDXAzgcd5jWlVrzVqe3ciekUlehhV4pF73xxvV93ys/vsLSvUspE1yGmX1mEugf6N5gSmVDu26Uug7btsH772ffbuHuhbyx8g38xI8ZETOoULRC7odTKhO9olcqh06dgtat4exZqFYNunfPul1UbBSDI+1s3m/c/gbtq7XPw5RKZdAreqVyqGRJGGVnFOa++2DPnj+3uZBygT6z+nD6wmm639yd51o/l7chlbqMFnqlrsMzz0DPnnDmDEREwPnzV77/t2//xsZjG6leojqf9/wcP9F/aso5+rdPqesgApMn21E4mzdfuTLVpI2T+HTjpwQFBPH1PV9TPKi4o1mV0kKv1HUqVgy+/tquTDV5sl24ZOPRjTz2rZ27Ztxd42h8U2NnQyqFFnqlbkjDhvDJJ7bYp/ol0Gd2Hy6kXODhJg/zQOMHnI6nFKCFXqkbNngw/LY7jW8KDSAqNoqm5Zry4Z03MFeCUm6mhV4pN5i67y0W7F5A8aDivH3LXAr4BTkdSalLtNArdYOW7V3Gi8teBGBogaXc1bYS//iHw6GUuowWeqVuwOGzh+n/VX/STBovtn2R28OacuECvPwyLFnidDqlLC30Sl2npNQk+s7uS8y5GDpU68Crt71K1662yBsDAwfCwYNOp1RKC71S1+25Jc+x5tAaKhatyPSI6fj7+QPw0kvQuTOcOGFnvUxKcjioyve00Ct1HWZtn8X7a98n0C+Q2X1nExoceuk9f3+YOhUqVYK1a+0c9ko5SQu9Ujm0M2YnQ+YPAWBsl7G0qNjiT21Kl4avvoLAQLtoiXbhKCfp7JVK5UB8UjwRsyKIT4qnf/3+PHbrY1dt26wZfPEFNGhgr+6VcooWeqVcZIxh6IKh7Dyxk7DSYfz37v8iItf8nv798yicUtegXTdKueg/v/yHGdtmEFIghDn95hBSICRH3//ZZ/DAAxmTnymVV/SKXikXrD64mqe+fwqAid0nUqd0nRx9//Hj8MQTEBcHTZrYr5XKK3pFr1Q2jsUfo+/svqSkpfBkiye5p949Of6MsmXtFT3Yuex/+snNIZW6Bi30Sl1Dcmoy/b7qx5G4I7St3JY3O7553Z8VEWGHWqakwD33QHS0G4MqdQ1a6JW6hr8v/Tsr9q/gppCbmNlnJoH+gTf0ef/8J7RpA0eO2Bu1KSluCqrUNWihV+oqvtrxFe+seYcAvwBm951NuSLlbvgzAwNh5kzblbN8Obz2mhuCKpUNLfRKZWFnzE4enPcgAG93eps2ldu47bPLl7fFvn59GDDAbR+r1FXpqBulMolLjKP3rN6XHop6vPnjbv8Zf/kLbNpkp0tQKre5dEUvIiVFJFJEEkRkv4gMzKZ9ARHZKSKH3BNTqbxhjGHI/CHsOrGLuqF1XXoo6npdLPLGwKxZcP58rvwYpVzuuvkISALKAoOAcSJS7xrtnwVibjCbUnnu3Z/fZfaO2RQpUIQ59+T8oajr8cor0K8fPHb12RSUuiHZFnoRCQYigJeMMfHGmFXAfGDwVdpXA+4F/unOoErlthX7V/DckucA+Lzn59xc+uY8+bl9+tjFxT/7DCZOzJMfqfIZV67oawMpxpjdl+3bDFztiv5D4AXgmr+IisgjIrJeRNbHxOjFv3LWwTMH6Tu7L6kmledaPUevsF559rMbNoTx4+3Xjz0GGzbk2Y9W+YQrhT4EOJtp3xmgSOaGItIL8DfGRGb3ocaYCcaYcGNMeGhoaHbNlco155PP03NmT6IToulQrQNvdHgjzzPcdx88+igkJtoHq06dyvMIyoe5UujjgaKZ9hUF4i7fkd7F8xbg/iEKSuWSizNSbji6gWrFqzGzz0wC/JwZjPbeexAeDvv22cKfluZIDOWDXCn0u4EAEal12b5GwPZM7WoBVYGVInIMmAOUE5FjIlL1xqMq5X5j14xl6tapBAcGM6//PEoVLuVYlqAgmD0bSpSwxf7ECceiKB+T7aWLMSZBROYAr4nIw0BjoAfQKlPTbcDlyyu0Av4DNEVH4CgPtPiPxTz3g735+kWvL2hQtoHDiaBqVViyBOrUgeBgp9MoX+Hq8MrhQCEgGpgODDPGbBeRtiISD2CMSTHGHLu4AaeAtPTXqbmSXqnr9MepP+j/dX/STBovtXuJ3mG9nY50yS23ZBR5Y+wUx0rdCJc6I40xp4CeWexfib1Zm9X3/AhUvJFwSuWGuMQ4eszowekLp+l+c3dG3zba6UhZunABHnkEVqyAX36BMmWcTqS8lc51o/KVNJPGfXPvY0fMDsJKh/Flry/xE8/9Z7B7N+zfb8faJyU5nUZ5K8/9G65ULhj942jm7ppL8aDizOs/j6IFMw8o8xxBQRAZCRUqwMqVdoy9LkOorocWepVvTNkyhTErxuAnfkyPmE6tUrWy/yaHlSsHc+faov/pp/Dhh04nUt5IC73KF1YdWMWQ+UMAeL/r+3St2dXhRK4LD4dJk+zXTz5pR+UolRNa6JXPi4qNotfMXiSlJjHi1hGMaDbC6Ug5NmAAvPCCfYjq7bedTqO8jc5Hr3za6Qun6TatGyfOneCOmnfwbtd3nY503caMsQ9TDR/udBLlbbTQK5+VnJrMPbPvYeeJndQLrceMPjMcm97AHfz84JlnMl6npdmROEFBzmVS3kG7bpRPMsbw+KLHWRK1hDLBZVg4cKFHj7DJqfPn7Rz2AwdCqj6OqLKhhV75pHfWvMP4X8dT0L8gc/vNpWrxqk5HcquDB+1N2chIeO45p9MoT6eFXvmcqVum8uySZwG7gEjLSi0dTuR+tWvDnDkQGAhjx8LHHzudSHkyLfTKp/wQ9QMPznsQgLGdx9Kvfj+HE+We22+H//7Xfv23v8E33zibR3kuLfTKZ2w6toneM3uTnJbMUy2e4smWTzodKdfdfz+8/LK9Mdu3L6xZ43Qi5Ym00CufsO/0Pu6YegdxSXH0q9ePf3f+t9OR8szo0fDgg/YG7TvvOJ1GeSLvHWumVLqT507SdUpXjsUf47aqt/F5z889eqIydxOBCROgbl0Y4X3Pgqk8kH/+NSifFJ8UT7fp3fjt5G80KNOAyH6RFAwo6HSsPBcQYMfYXxxTn5wMp087m0l5Di30ymtdSLkUd9qIAAAT0klEQVRAzxk9+fnQz1QuVplvB31L8aDiTsdy3Llz0KsXdOkC8fFOp1GeQAu98krJqcn0/6o/S/cupWxwWX4Y/AMVi+o6NwBnz8KOHXaxkogIncdeaaFXXijNpPHgvAeZ99s8SgSV4PvB33vFlMN55aabYPFiCA2F77+H/v1tV47Kv7TQK69ijOGxbx5j6tapBAcGs2jQIhqWbeh0LI9Tq5Yt8sWL26dnBw/WqRLyMy30ymsYY3j+h+cvTW2wYMACmlds7nQsj9W4sb2yL1IEZs6Ehx6y4+1V/qOFXnkFYwwvLnuRt1a/RYBfALP7zqZ9tfZOx/J4zZrBokUQHAwnTmgXTn6l4+iVx7tY5P+56p/4iz/Tek/j7pvvdjqW12jdGlatsuPsCxRwOo1ygl7RK4+WucjP6DODvvX6Oh3L6zRunFHkL1yAceN0ofH8RAu98lhZFfk+dfs4HcvrDRxoV6kaNkz77PMLLfTKIxlj+PvSv18q8jP7zNQi7yaPPmqfoP3kE3uDVkfj+D4t9MrjpJk0hn8znDd/evNSkY+oG+F0LJ/RpQt8+y0ULgyffw733qs3aX2dFnrlUZJTkxkcOfjSEMrIfpFa5HNB+/YZQy9nzLDLEiYmOp1K5RYt9MpjnE8+T+9ZvZm2dRohBUJYNGiRjq7JRW3awA8/ZDxU9d57TidSuUULvfIIcYlx3DntThbuXkjJQiVZdt8yHSefB5o1g+XLbffNk76/Tku+pePoleOOxh2l2/RubDi6gXIh5VgyeAn1ytRzOla+0bgxfPllxuu4OPtwVbVqzmVS7uXSFb2IlBSRSBFJEJH9IjLwKu2eFZFtIhInIntF5Fn3xlW+Znv0dlpMbMGGoxuoUaIGqx5apUXeQUlJ0Ls3tGwJGzc6nUa5i6tdNx8BSUBZYBAwTkSy+tcowH1ACaArMEJE+rsjqPI9y/cup/Wk1hw4c4AWFVuwZsgaqpeo7nSsfO3ilMbHj8Nf/mKnT1DeL9tCLyLBQATwkjEm3hizCpgPDM7c1hjzljFmgzEmxRjzGzAPaO3u0Mr7TdkyhS5TunAm8Qy9w3qz7L5lhAaHOh0r3wsJgYUL7dTGcXHQrRt8+KE+RevtXLmirw2kGGN2X7ZvM3DN369FRIC2wPbrj6d8TZpJY/SPoxkcOZjktGSebPEks/rMolBgIaejqXQFC8LUqfDyy/bJ2ccfh8ce07H23syVQh8CnM207wxQJJvvG53++Z9l9aaIPCIi60VkfUxMjAsxlLeLS4yjz6w+vPq/VxGE97q8x9guY/H383c6msrEzw9efRWmTLGFf9w4+O9/nU6lrpcro27igaKZ9hUF4q72DSIyAttX39YYk+VjGMaYCcAEgPDwcP3F0MdFxUbRY0YPtkVvo1jBYszoM4OuNbs6HUtlY9AgqF4dxo+HRx5xOo26Xq5c0e8GAkTk8rXaGnGVLhkReQh4HuhgjDl04xGVt1satZRb/3sr26K3Uad0HX4Z+osWeS/SsqWdKiEg/bLw+HGYO9fZTCpnsi30xpgEYA7wmogEi0hroAfwZea2IjII+AfQyRgT5e6wyrukmTTeWPEGnad05tT5U3Sr3Y21D6+ldqnaTkdT1yk11d6o7dULnnkGUlKcTqRc4erwyuFAISAamA4MM8ZsF5G2IhJ/WbvXgVLAOhGJT9/Guzey8gYxCTHcOfVORi0fRZpJY1TbUczrP4+iBTP3Aipv4udni3xAALzzDnTsCMeOOZ1KZUeMB4ybCg8PN+vXr3c6hnKTVQdW0f+r/hyOO0ypQqWY0nuKdtX4mFWroG9fW+TLlLFdO131FOc5EfnVGBOeXTud60a5TWpaKv9Y+Q9um3wbh+MO07pSazb9dZMWeR/Upg1s2GBnwYyOhjvugGf1OXiPpYVeuUVUbBTtJrfjxWUvkmpS+b/W/8fy+5dTsWhFp6OpXFKuHCxZAv/4B/j72wXIlWfSSc3UDTHGMGnjJEYuHkl8Ujzli5Tnsx6f0blGZ6ejqTzg7w9//zvceSfUu+wRyt9/hxo1bJ++cp6eBnXdjsYdpdfMXjy84GHik+LpW7cvW4dt1SKfDzVqlDH8MjoaWrWy3Tp79jibS1la6FWOGWOYuGEidT+uy7zf5lGsYDGm9JrCzD4zKVmopNPxlMP27LFX8itWQMOG8MEHugi507TQqxz5/eTvdPiiAw8veJjTF05zR8072DJsC4MaDsJOb6Tyu5YtYccOGDgQzp2DJ56wM2Fu2+Z0svxLC71ySWJKIv9Y+Q8ajm/I8n3LKV24NNN6T+Obgd9QuVhlp+MpD1OqlJ0YLTISypa1wzGbNLEzYaq8p4VeXZMxhoW7F1Lv43q8uOxFLqRc4L5G97HzsZ0MaDBAr+LVNfXsCTt3wrBhtvumSROnE+VPWujVVe0+uZu7pt3F3dPvZk/sHsJKh/HD4B/4vOfnlC5c2ul4ykuUKAEff2z77tu0ydj/r3/Bli3O5cpPtNCrPzl57iRPL36a+h/XZ9EfiyhWsBjvdXmPzX/dTIfqHZyOp7xU1aoZX69ebYdlNm4MQ4bA4cOOxcoXtNCrS+KT4nl9xetU/6A6Y38eS0paCkOaDGH333bzRIsnCPQPdDqi8hG1a9sFTfz9YdIkqFXLLnQSd9XJz9WN0EKvSEpN4qNfPqLmBzV5aflLnE08S9eaXfn1kV/5tPunlAku43RE5WNKl4b337ejcyIi4Px5GDPGzn3//vtOp/M9+mRsPnY++TwTN07krZ/e4uDZgwA0r9Ccf3X8F7dVvc3ZcCpfqFULvvoKfvoJnnvOdulE6QTnbqeFPh+KT4pn/PrxvL36bY4nHAegXmg9xrQfQ886PXUkjcpzrVvbIZhLlkD9+hn758yB336Dv/7V3tRV10enKc5HjsQd4eN1HzNu/ThOnT8FQNNyTRnVdhQ96vTAT7QnT3mO1FSoWxd277YTpg0ZAiNHQrVqTifzHDpNsbrkl8O/MGjOIKq8V4U3Vr7BqfOnaFWpFd8O/Jb1Q9fTK6yXFnnlcfz87ANWnTtDQoKdSqFmTbjnHlizBjzgGtVr6BW9jzqffJ6vd37Nx+s+Zs2hNQD4iR+9w3rzRPMnaF2ptXbRKK+xeTOMHQvTpmUsXzhvHnTv7mwup7l6Ra+F3sdsOLqBiRsmMnXrVM4kngGgRFAJhjYdymPNHtPpCpRXO3QI/vMfmD8fNm6EggXt/ilTICwMmjaF/HT9ooU+H4lOiGbW9llM2jiJjcc2XtrfrEIzhjQZwqAGgwguoKtCKN9hTEZBP3MGKlSw3TthYTB4sJ1QrUoVZzPmBS30Pi72fCyRuyKZsW0GS/cuJc3YeWBLFirJ4IaDGdJkCA3KNnA4pVK5LyYGXn/dduucOJGx/y9/gXvvhX79oEgR5/LlJi30PigmIYZvfv+GOTvn8N0f35GclgxAoF8gXWt2ZVCDQfSs05OCAQUdTqpU3ktOhsWLbTfOvHlw4YLdv2ePfRAL7L6gIOcyupurhV7H0XswYwy7Tuxi/m/zWbB7AasPrsZg/8fsJ350rN6R/vX60yusly74ofK9wEDo1s1uZ87YMfhr12YUeYDwcHt136uXXdC8fv380aevV/QeJvZ8LD/u+5Efon7g+6jv+ePUH5feK+BfgPZV29P95u5EhEVQNqSsg0mV8i5Hj9qif/FKH6B8eejSJWMrXty5fNdDu268xLnkc6w9tJYfon7gh70/sP7I+kv97QClCpXirtp30b12dzrX6EyRgj7a2ahUHkhIgO++gwULbDfPsWMZ7y1aBF272q/37bNP4hYr5khMl2nXjYc6EneEnw78xOqDq/np4E9sPLaRlLSUS+8H+gXSpnIbOlbrSIfqHWhWoRkBfnqalHKH4GA7iVpEhB25s2WLLfhLl9qbtxeNHGmHcDZqBO3a2a1VKyhXzrnsN0Kv6HNR7PlYNh7byIajG/j16K+sObiG/Wf2X9HGT/xoWLYht1e9nY7VO9K2SltCCoQ4lFgpBfZBrO++szd4L1e+PDz1FDz9tDO5MtMr+jyUZtI4cOYA26O3s+nYJjYc28CGoxvYd3rfn9oWKVCElpVa0rpSa1pVakXzCs21O0YpDzN/vp06ee1aWLHCbuvWwZEjV7b77jsYMQIaNoQGDTK2mjXtXPueQgt9DqSkpRAVG8XOmJ3siNnBjhM72BGzg10ndnEu+dyf2gcFBNGobCOalmtKk5ua0Lxic+qF1sPfz4P+BiilslSoENx2m93Arnn7++9X3rBdt84O39yzxy6EflFQENSrZ+fkCUxfrycqynb9FCqUV0eQQQt9JmcTz7Ln1B6iYqPYE3vln/tP7yfVpGb5fWWDyxIWGkbjso1pUq4JTcs1pU7pOtq/rpSP8PODm2++ct/zz0OPHrB165XbwYMQG5tR5MFOxXzsGFSqZOfhr1XL3gMYNiz3s+erKnQ28SyHzh7Kcjscd5iDZw4SeyH2mp9RqWgl6obWpW5oXcJKh9k/Q8N0HLtS+VBgoO22adjwyv2nT9vhnBclJkLRovbJ3YMH7bZsGdxyixb6bCWnJnPi3AmiE6Kv2GLOxfxpX3RCNAnJCdl+ZqGAQlQvUf3SVqNEDftnyRpULV6VoAAfeqxOKZUrihe/sounYEG7gEpyMuzfb7uAdu+2xT8vuFToRaQkMBHoDJwA/m6MmZZFOwH+BTycvutT4HmTS0N7hi4YyuebP3e5faGAQlQqVomKRSvarUjFS19XKFqBikUrUrpwaZ2bXSmVKwID7Y3amjXtk7l5xdUr+o+AJKAs0Bj4RkQ2G2O2Z2r3CNATaAQYYAmwFxjvnrhXKl+kPGWCy1yxhRYOzXJfaHAoxQoW0znYlVL5Trbj6EUkGIgF6htjdqfv+xI4bIx5PlPb1cBkY8yE9NdDgKHGmBbX+hm+Oo5eKaVykzuXEqwNpFws8uk2A/WyaFsv/b3s2imllMojrhT6EOBspn1ngKye8glJf+/ydiGSRX+JiDwiIutFZH1MTIyreZVSSuWQK4U+Hsh8b7goEOdC26JAfFY3Y40xE4wx4caY8NDQUFfzKqWUyiFXCv1uIEBEal22rxGQ+UYs6fsaudBOKaVUHsm20BtjEoA5wGsiEiwirYEewJdZNP8CeEpEKohIeeBpYLIb8yqllMohVweMDwcKAdHAdGCYMWa7iLQVkfjL2n0CLAC2AtuAb9L3KaWUcohL4+iNMaew4+Mz71+JvQF78bUBnkvflFJKeQB9BFQppXycRyw8IiIxwP5sG2atNHZaBl+gx+KZfOVYfOU4QI/loirGmGyHLXpEob8RIrLelSfDvIEei2fylWPxleMAPZac0q4bpZTycVrolVLKx/lCoZ/gdAA30mPxTL5yLL5yHKDHkiNe30evlFLq2nzhil4ppdQ1aKFXSikf5xWFXkRKikikiCSIyH4RGXiVdiIib4rIyfTtzaymSHZSDo5ltIgki0j8ZVv1vM57NSIyIn2a6UQRmZxN2ydF5JiInBWRSSJSMI9iZsvV4xCRB0QkNdP5uC3vkmZPRAqKyMT0v1dxIrJJRK66YJ2nnpecHIeXnJcpInI0/b/zbhF5+Bptc+WceEWh58qlDAcB40QkqwVNLl/KsCFwN/BoXoV0kavHAjDTGBNy2RaVZymzdwR4HZh0rUYi0gV4HugAVAGqA6/mejrXuXQc6dZkOh8/5m60HAsADgJ/AYoBo4BZIlI1c0MPPy8uH0c6Tz8v/wSqGmOKAt2B10XklsyNcvOceHyhT1/KMAJ4yRgTb4xZBcwHBmfR/H7gHWPMIWPMYeAd4IE8C5uNHB6LRzPGzDHGzAVOZtP0fmCiMWa7MSYWGIMHnZMcHIfHM8YkGGNGG2P2GWPSjDELsWs2/6mo4MHnJYfH4fHS/xsnXnyZvtXIommunROPL/T41lKGOTkWgLtF5JSIbBeRYbkfL1dkdU7Kikgph/LciCYiciL91++XRMSlSQGdIiJlsX/nsloTwmvOSzbHAV5wXkTkYxE5B+wCjgLfZtEs186JNxT6XFnK0CE5OZZZQBgQCgwFXhaRAbkbL1dkdU4g62P2ZCuA+kAZ7G9lA4BnHU10DSISCEwFPjfG7MqiiVecFxeOwyvOizFmOPa/bVvs+h6JWTTLtXPiDYU+V5YydIjLx2KM2WGMOWKMSTXGrAbeB/rkQUZ3y+qcQNbnz2MZY6KMMXvTuxK2Aq/hoedDRPywCwMlASOu0szjz4srx+FN5yX93/IqoCKQ1W/ouXZOvKHQ+9JShjk5lswM4Cm/meREVufkuDHG2/vEPfJ8pP/2OhF7sz/CGJN8laYefV5ycByZeeR5ySSArPvoc+2ceHyh96WlDHNyLCLSQ0RKpA8ZbQY8DszL28RXJyIBIhIE+AP+IhJ0lb7RL4AhIlJXRIpjR1BMzsOo1+TqcYjIHel9xYhIHeAlPOh8XGYctsvvbmPM+Wu08+jzgovH4ennRUTKiEh/EQkREf/0kTUDgKVZNM+9c2KM8fgNKAnMBRKAA8DA9P1tsV0zF9sJ8BZwKn17i/RpHjxly8GxTMeOBInH3sB53OnsmY5jNBkjCC5uo4HK6ZkrX9b2KeA49v7EZ0BBp/Pn9DiAt9OPIQGIwnYRBDqdP9OxVEnPfyE9+8VtkDedl5wch6efF+w9tv8Bp9P/O28Fhqa/l2fnROe6UUopH+fxXTdKKaVujBZ6pZTycVrolVLKx2mhV0opH6eFXimlfJwWeqWU8nFa6JVSysdpoVdKKR+nhV4ppXzc/wNjO3dcMU3YbgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fc0a080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris-Virginica\")\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris-Virginica\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure in the book actually is actually a bit fancier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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5MgA3b+a+f49SfIVFh7Hj8g52XtnJrqu7nhlDkzp77KVqL9G6amu1V9dzQiU4ipKFTZu08Tu7d0NgIOzYAVevaosUVqmSnuDcvq1NXW/ePH3bCqXkCA8PN3QISj4kJSdx+OZhtlzYwpYLW55Zy8jZzplONTrRsUZHOlTvoFponlPqR7KiZMPJCfr21Q4p4eJF2LYN2rVLr7N2LXz4oba7+yuvwOuvQ5cuYGdnuLiVvAsLCzN0CEoeRcVGsePyDrZc3MK2i9uIeByR9p61qTUvV3+ZTjU60almJ9zKu6kxNIpKcBQlL4SAOnW0IyMLC63swgVtAPPq1doaPC+/rM3eSh3voxRPqV1USvEUGhXKxnMb+f387+y9vjfTBpTVy1Sna52udK3TFS9XLzVlW3mGmkWlKHpw+bK28vLvv8M//0BystaS88cf2vuJiVoSVL++YeNUlOLu8r3LrD+7nvVn13Mo7FBaubEwprVLa7rW1pKaug51VStNKadmUSlKMVCzJnzyiXZERGi7q1epkv7+P/9os7EaNEjv9nq6NUgpej4+PgAsXrzYwJE8385EnGH9GS2pyTiexsrUii61utCzXk+61OqiBgcrOlEtOIpSBFatghEj4P799LKGDbVurL59oUYNw8X2PEttAShNPwdLisv3LrPy5EpWnVrF2cizaeW2ZrZ0c+tGr3q9eKXWK1iZqtU3n1clqgVHCFEO8Af+A0QCvlLKlVnUMwfmAm8ApsA+YJiUUo0IVEqk/v2hVy/YtQvWrIGNGyE4WDsWLICQEG2cj1K0Fi1aZOgQniu3H91mzek1rDy5koNh6RuElrMsRw+3HvSq14uONTqq8TSKXhRpC44QYhVgBAwBGgJbgVZSytNP1RsDvIWWCEUBiwEbKWXPnO6vWnCUkiIuDv78U0t2ataEL77QyiMjtXV23noLevYEG7Vvn1LCRcdFs/HsRlaeWsn/rvyPZJkMgI2ZDW/UfYMBLwygQ/UOmBqbGjhSpbgpMVs1CCGsgfuAu5TyQkrZMiBMSjnuqboLgYdSyjEp568B30op3XJ6hkpwlJLuhx+0aeegbSzasye88442fketoqyUFMkymV1XdhEQHMBv534jNjEWAFMjU7rU7sIA9wF0c+umup+UHJWkLqo6QGJqcpPiOOCVRV1/YK4QojLwAK01Z1tWNxVC+AA+AC4uLnoNWFGK2sCBYG4OP/+s7Ze1bJl2VKmiJTpffqm6svRp8+bNAHTr1s3AkZQOV+9fZWnwUpYeX0pIVEhauZerFwNeGECver0ob1XegBEqz5OiTHBsgOinyqIA2yzqXgRCgTAgCTgJjMzqplLKxWhdWHh6eqqRgkqJVqYMDB2qHZcva8nNL79oqygfOZKe3EipdXNZWBg23pKue8o+HWqQcf49SXjChrMbCAgO4K+rf6WVVy9TnXcbvot3Q29c7NUfn0rRK8oE5xHw9PqudsDDLOrOB8yB8kAMMAatBad5YQaoKMVJzZowZQpMnqy15mTsotq/H7p2hbff1pIhd3eDhVmide3a1dAhlFjBt4JZdGQRq06tIiouCgALEwt61+/N4IaD8armhZEwMnCUyvPMEGNwGkgpL6aU/QLczGIMzilggpTy95TzMinXOkopI7N7hhqDozwvpkwBP7/085YttUSnTx9t7I6iFIbYxFjWnVnHgsML2H9jf1p5syrNGNxwMH3d+1LGoowBI1RKkxIzyBhACLEakMB7aLOo/iDrWVRL0Fp3BgOPgc+AEVLKKuRAJTjK8yQoCH78EVasgIcp7aB2djBqVObkR1EK6sr9Kyw6sgj/Y/7cfXIXADtzO7w9vPFp4oN7BdWEqOhfSRpkDDAcCADuAHeBD6SUp4UQbYFtUsrUSbGjge/RxuKYAafQ1sRRFCVF48awcCHMnq1NN//xRzhwAGJi0uskJGhdW0aqp0DRUVJyEn9c/IMFRxbw56U/kWh/DDeq2IgPPD9gwAsDsDZTzYVK8aVWMlaUUiQoCCpUAGdn7XzRIvjmG20V5UGDwN7eoOEVO2ol42dFx0XjH+TP94e+59qDawCYG5vT170vwz2H06xKM7UHlFIkSlQXVWFTCY6iZNalC2zfrr22sdGmmn/0EbjluKLU80MlOOmu3r/K9we/x/+YPw/jtT7PGmVrMNxzOIMaDlLTu5UipxKcDFSCoyiZJSbCpk3aAoKBgenl3bvDxIngme8fHUppIKVkX+g+5hyYw2/nfktbZdjL1YuPW3xM1zpdMTZSK0wqhlHSxuAoilKETEy01ZB79oRTp+D777V1dTZt0spUgvN8SkhKYO2Ztcw5MIcjN7U/Ck2NTBn44kBGNR9Fo0qNDByhohScasFRlOfMnTvw008wejSYmWllM2dqXViDBqlp5qXZ44THBBwLYPa/s7kedR2A8pbl+cDzA4Y3HU4l20oGjlBR0hVpF5UQ4nVgs5QyKb8PLEwqwVEU3d27By4u2uyrcuVg+HBtnI6jo6EjK3ypWzSkbtlQWt1/cp8Fhxcw9+BcIh5HAFCnfB1GtxzNwBcHYmlqaeAIFeVZRZ3gxKCtPPwz4P/UvlIGpxIcRdFdUhL89hvMmgUHD2plVlbw/vtaK0/lyoaNrzCV9kHGNx/eZM7+Ofz36H95FP8IAM/Knvi28aWHWw81vkYp1oo6wbEFBgDvAk2B/WgbY/4qpYzJ6dqioBIcRck/KbUtIb76CrZu1crMzODCBXB1NWxshaW0brZ58e5FZv07i5+P/0x8UjwAHWt0xLeNL+2rtVfTvJUSwWCzqIQQDdBWGn4LsALWoLXqHMhvMAWlEhxF0Y9jx2D6dIiKgh070stDQ6FqVcPFpeTsXOQ5pu6dyupTq0mWyQgEver3YmzrsXhWViPKlZLFoNPEhRDOgA/aZpjxgCUQBAyVUp7I943zSSU4iqJfCQlgaqq9PnIEmjeHXr1g/Hho2NCwsSnpzkacTUtsJBJTI1Pe8XiHMa3HUKd8HUOHpyj5UtAER+cF3IUQpkKIPkKI7cBV4GVgGOAEuAJn0VpzFEUp4VKTG9BWSTYxgbVroVEjbZr5iSL/M0a/Fi9ezOLFiw0dRr6dvnOafuv60WBBA1adWoWJkQnDmgzj4ocX+an7Tyq5UZ5ruo7BmQf0R9swcxnwk5TyzFN1KqLtEF7ku9+oFhxFKVxhYdpg5EWLIDZWK3vzTW138/r1DRpavpTUQcan7pxi6t6prD29Nq3F5r3G7zGuzThc7F0MHZ6i6EVRL/RXHxgJbJBSxmdTJxJon9+AFEUpvqpUge++g7FjtcHIixZpLTqOjjB/vqGj093QoUMNHYJOTt85jd8eP9aeWQuAmbEZ7zXSEpuq9mpwlKJkpGsLTjvgXyll4lPlJkArKeVePcenE9WCoyhF68YNLdHx9dWSH9B2NHd0hJo1DRtbaXL53mWm7JnCihMrkEjMjM0Y2ngo49qMw9nO2dDhKUqhKOpp4klAJSnlnafKywN3pJQGXVRBJTiKYlhJSfDCC9rU8kGD4PPPoVo1Q0dVct18eJOpe6by07GfSExOxNTIFJ8mPiqxUZ4LRd1FJdDG3zytPGDwdXByEx0dzZ07d0hISDB0KIqCqakpFSpUwM7OztCh6E1MDLRooSU4/v6wbBl88AFMmFA8V0a+efMmAJWL2WqGdx/fZea+mcw7NI/YxFiMhBGDGg5istdkqpWpZujwFKVEyFMLjhBiU8rL14D/AXEZ3jYG3IGzUspX9B6hDnJqwYmOjub27dtUqVIFS0tLtdCVYlBSSp48eUJYWBhOTk6lKskBuHgR/Pxg5UptAUEbG21V5M8+01ZJLi6K2yDjh3EP+e7Ad8zeP5vouGgAetXrxdT2U6nnWM/A0SlK0SqqaeJ3Uw4B3M9wfhe4AfwXGJjfIIrCnTt3qFKlClZWViq5UQxOCIGVlRVVqlThzp07uV9QwtSuDcuXQ3AwvPoqPHqkDUgubipVqkSlSobfYDI2MZY5++dQ4/saTNo9iei4aDrX7MzhoYdZ12edSm4UJR/y1EUlpXwXQAhxDZhdHLZl0FVCQgKWlmpDOaV4sbS0LNVdpi++qG37sHcvPHiQ3noTHQ2bN0O/fmBswJF7qV1UhpKUnMQvx39h0u5J3Ii+AUCrqq2Y/vJ0vKp5GTQ2RSnpdFqrRkrpVxKTm1Sq5UYpbp6X78l27aB79/Tzb76BgQO1BQO3btW6sZ4nUkq2X9pOo0WNGLxpMDeib+Dh5MGW/lv4591/VHKjKHqQa4IjhDghhCib8vpkynmWRx7uVU4IsVEIESOEuC6EGJBD3cZCiL1CiEdCiNtCiP/T7aMpilJc1a2r7Wl18iR07aolQAcMtotd0ToWfoxOyzrRZUUXTt45iYu9C8vfWE7Q+0G8Vue15ybpVZTClpcuqvWkDypeV8DnzUfbs8oJaAhsFUIcl1KezlhJCOEAbAc+TnmmGaDmRCpKKdG/P7zxBixcCF9+Cf/8Ay1bQt++MGMGVK9eNHE0adIEgKNHjxb6s64/uM7EwIksP7EciaSMRRkmtJ3AyGYjsTCxKPTnK8pzR0pZJAdgjZbc1MlQtgz4Kou604Fluj6jSZMmMjtnzpzJ9r2SzsvLS44YMaLQn+Pq6ipnzZpV4PsEBgZKQEZEROT5miVLlkhra+sCP7s4Ks3fm3kRFSXl+PFSWlhICVJu2VJ0z0Zb9qJQn3H/yX352Y7PpPlUc8kUpNlUM/nJ9k/k3cd3C/W5ilLSAUdkAfKOotwvqg6QKKW8kKHsONAgi7otgHtCiH+FEHeEEJuFEM/lBiuDBg2ia9euOdbZsGEDM2bMyNf9P/roI2rXrp3le/fv38fS0jJtM8LDhw8zfPjwfD0no1atWhEeHk758uXzfE3fvn25cuVKgZ+tFD92dlorzvnzWuvNq6+mv/e//0F8dpvC6MGRI0corMVB4xLj+O7Ad9T8viaz/p1FXFIc/d37c27EOb7p/A3lLMsVynMVRdHk2kUlhDhJ1ov7PUNK+WIOb9sA0U+VRQG2WdR1BhoDnYCTwNfAKqB1FvH5AD4ALi7PVw4UHx+PmZkZ5crl/wflkCFDmDdvHnv27MHLK/PAxhUrVmBsbEz//v0BcMxlpbbUeHJjZmZGxYoVdYrT0tJSzYIr5VxcYNy49POTJ6FzZ627auZMbfdyfQ9PSe2i0icpJb+e/hXfXb5cfXAVAC9XL2Z1mkXTKk31/jxFUbKWlxacdWjjcPJy5OQR8PRqZnbAwyzqPgE2SikPSyljAT+glRDC/umKUsrFUkpPKaVnbr+AS7rU1pyZM2fi7OyMs7M2LOmll15i5MiRafU2bNjAiy++iKWlJeXKlcPLy4vbt29neU8PDw88PT0JCAh45j1/f3/69OmDra2Wg1arVo3Zs2envS+EYP78+fTs2RNra2vGjx8PwNatW3Fzc8PCwoJ27dqxevVqhBBcu3YNgN27dyOEIDIyEoClS5diY2PDrl27cHd3x9ramvbt23P16tW0Z6XWyeiPP/6gefPmWFpaUr58ebp160ZsyhbXy5cvp2nTptja2lKhQgXefPNNwsLCdPr3Vgzr4UNtPZ3Ll6F3b2jbFg4eNHRUOTt44yCtAlrRb30/rj64Sj2Hemzuv5lA70CV3ChKEcu1BUdK6aenZ10ATIQQtaWUF1PKPIDTWdQ9QeZWo0KZRCr8DDNbQU7O/8fZs2cP9vb2bN++PcvVV2/dukW/fv2YMWMGvXr14tGjRxzIZXrKkCFD+PTTT5k3b17airpBQUEEBwfzww8/5Hitn58f06dPZ/bs2QghCAkJoWfPnowYMYL333+fkydP8sknn+T6ueLi4pgxYwYBAQFYWFjg7e3NsGHD+PPPP7Osv337drp37864ceNYsmQJiYmJ7Nixg+TkZEBrTfLz86Nu3bpERkYyduxY+vfvz969Bt0PVtFBq1ZaK85PP8HkybBvn7YNhD4HIk+ZMiXT1/wKjQrFd5cvK06uAMDJ2omp7afybqN3MTHSdUccRVH0ocj+z5NSxgghNgBfCCHeQ5tF1QNolUX1JcB6IcT3aAnQROAfKWVUUcVbXFlYWBAQEIC5uXmW79+8eZOEhAR69+6Nq6srAO7u7jnec8CFGoNCAAAgAElEQVSAAXz66aesXr0aHx8fQGu9qVu3Lq1bP9MrmEnfvn1577330s59fX2pUaMG3377LQBubm5cuHCBCRMm5HifxMRE5s+fj5ubGwCjR49m8ODBSCmznDY7depUevfuzbRp09LKXnwxvYd08ODBaa9r1KjBwoULqVevHjdu3Ehr+VKKP1NTbS+rAQO0bqo5c2DNGjAzg19+Kfj9/fy0v9/ym+A8TnjMrH2zmLlvJk8Sn2BubM4nLT/Bt40vtuZZ9b4rilJU8jIG5wTgJaW8n9t4nFzG4AAMBwKAO2jbPHwgpTwthGgLbJNS2qTc5y8hxHhgK2AF/ANku2ZOfhWkJcVQ3N3ds01uQOty6tixI+7u7vznP/+hY8eO9O7dG0dHR0JCQqhfv35a3fHjxzN+/Hjs7Ox48803CQgIwMfHh9jYWFauXJlrUgLg6Zl5m5Bz587RtGnmpvjmzZvneh9zc/O05Aa0zQ/j4+O5f/9+lmOMjh07xqBBg7K9X1BQEH5+fgQHB3Pv3r201q6QkBCV4JRA9vYwfToMG6a15mTMR8LDoUKF/K2IPHny5HzFkyyTWXVyFeN2jUtbgfjN+m8ys+NMqpctojnuiqLkqEjXwZFS3gNez6L8b7RByBnLFgILC/K80sja2jrH942NjdmxYwcHDhxgx44d+Pv74+vry549e2jQoAHBwcFpdTMmDkOGDKFdu3acOXOG4OBgYmJi8Pb2LnA8eWVikvlbMbXVJrXLSRcxMTF07tyZjh07smzZMipUqEBkZCRt27YlvjCn5CiFzsUFlixJP09Kgtde017PmQNeOi4AnJ+WmwM3DjBq+ygOhmkDghpXasx3nb+jrWtbne+lKErh0WkMjh7H4yiFSAhBy5YtadmyJZMmTaJBgwasWbOG6dOnU6tWrSyvadu2LW5ubvj7+xMcHEz37t1znTWVlbp16/L7779nKjt06FC+PkdOGjVqxK5duxg6dOgz7507d47IyEimT59O9ZSBGhs2bNB7DIrhXb8OkZEQGgovvQS9esHXX0ONGvp/VmhUKON2jWPlyZUAVLSpyIwOM3jH4x2MRFGuuKEoSl7k6/9KIURNIUTXlKOmvoNS8u/AgQNMmzaNw4cPExISwqZNmwgNDc3UNZWdwYMHExAQQGBgIEOGDMnX84cNG8bly5cZPXo058+fZ8OGDSxK2UZan0vQT5gwgbVr1/L5559z5swZTp8+zZw5c3j8+DEuLi6Ym5vzww8/cOXKFbZu3crEiRP19myl+KhRA86dgy++0DbyXL8e6tUDX19tQ8/cHD16NNdVjGPiY5gcOBm3H9xYeXIl5sbmTGg7gYsfXmRQw0EquVGUYkqn/zOFEOWFEL8BF4HfUo4LQojfhRB5X7VNKTT29vbs27ePrl27Urt2bT799FMmTpzIwIEDc73W29ubmJgYnJ2d6dy5c76e7+rqyvr169m0aRMeHh7MmTMnbZyDhYX+lqN/9dVX2bhxI9u2baNRo0Z4eXkRGBiIkZERjo6O/Pzzz/z222/Ur18fPz+/tEHPSuljZQUTJ8KFC/D229rCgF99pc24yq2H09PT85lxZKmSZTLLji+jzg91+GLvFzxJfELfBn05N/Ic016eho2ZTZbXKYpSPIisphpnW1mIjUBt4H0gdUWK5mhjZS5JKXvqPUIdeHp6yuxWJT179iz16tUr4ogUgLlz5zJp0iQePHigNhLMgvre1K9Dh2DUKOjXDz76SCuTMutFArPbi+rf0H8ZtX0Uh28eBsCzsidzOs+hjUubQo1dUZR0QoijUsqs/wLJA12niXcGOkgp92co2yeEeB/4X36DUEqX+fPn07RpUxwdHTlw4ABTp05l0KBBKrlRikSzZtqaORlbb2bP1hKfr7/OvH7O04nN9QfXGbdrHKtPrQagkk0lvur4FQNfHKi6ohSlhNE1wYkAYrIof4w27VtRuHTpEtOnT+fu3bs4OzszbNgwJk2aZOiwlOeIEOnTxuPj4dtv4dYt2LwZPvlEG6Njm2GZmkfxj5j5z0xm759NbGIsFiYWfNbqM8a0HqO6ohSlhNK1i2oI8BbwtpQyLKWsCvAzsFpK+VOhRJlHqotKKYnU92bhu3FDS2qWL9fOK1bU1tV5+51kVpxchu8uX8IfhQPQz70fMzvOxMX++drbTlGKm0Lvospicb/qwDUhROrGPlWAWKACYNAER1EUJSvOzrBsGYwcqY3POXAABg+GwWODwfszsImgaeWmfPfKd7SqmtXi6oqilDR56aIq0OJ+iqIoxUXz5rDqj+v0n7KJA0tfB/M4SIpg2RvLGPDCADXORlFKkaLcbFNRFMVgMo2zKReL+agpvFX1//DtdJFarrW4fFnb2NPXF1L2nFUUpQRT29wqilKqJctklp9Yju8uX24+vAlAf/f+fNXxq0zjbD77DDZu1LaC+PJLGDQof/tbKYpSPOi60J+ZEMJPCHFBCBErhEjKeBRWkIqiKPmxL2QfzX9qjvdv3tx8eJOmlZuyb/A+VvZa+cwg4rFjtcUBb9+G994DT0/Ys8dAgSuKUmC6djhPBbyBb4Bk4DNgPtoU8eH6DU1RFCV/QqJC6L++P22WtOHIzSNUtq3ML6//woH3DmQaROzj44OPjw+gjc/5919YuRKqVoXg4PT9ra5fN9AHURQl33RNcPoAw6SUi4Ak4Hcp5UfAZKCTvoNTireXXnqJkSNHFvpzqlWrxuzZswt8n927dyOEIDIyMs/XLF26FBsbtQ5KSRETH8OkwEm4/eDG6lOrsTCxYGK7iZwfeZ63Pd5+ZhDxjz/+yI8//ph2LgT07595f6tNmyA2tqg/iaIoBaVrguMEnEl5/Qgok/J6O/AffQWlpEtdAXjq1KmZyvPzyzqvCcmgQYPo2rVrrvU2bNjAjBkz8vz8jD766CNq166d5Xv379/H0tKSxYsXA3D48GGGDy94A2GrVq0IDw+nfPm8b5vWt29frly5UuBnK4Ur475RU/dOJTYxln7u/Tg34hxftP8i28X6Fi1alLYZbEYZ97f65Rdwc9PKpdTG6SSpDnlFKfZ0TXBCgMopry+hbd0A0BJ4oq+glMwsLCyYNWsWERERhg4FgPj4eADKlSuHbcblYHUwZMgQLl26xJ4sBjmsWLECY2Nj+vfvD4CjoyNWVla5xpMbMzMzKlasqNOWEZaWllSoUCHP9ZWitz90Py39W/LOb+9w8+FNPCt78s+7/7Cq1ypcy7jmeG3GLqqsVKmiteikWr8eevaEJk1g9249fQBFUQqFrgnORqBDyuu5gJ8Q4iqwFLXIX6Fp37491apVe6YV52l79+6lefPmWFhY4OTkxMcff5z2y3/QoEHs2bOH+fPnI4RACMG1a9fy9PzUFp2ZM2fi7OyMs7Mz8GyL0IYNG3jxxRextLSkXLlyeHl5cfv27Szv6eHhgaenJwEBAc+85+/vT58+fdKSp6e7qIQQzJ8/n549e2Jtbc348eMB2Lp1K25ublhYWNCuXTtWr16d6XM+3eqV2v20a9cu3N3dsba2pn379ly9ejXtWVl1Uf3xxx80b94cS0tLypcvT7du3YhN6cNYvnw5TZs2xdbWlgoVKvDmm28SFhaGon+hUaEMWD+AVgGtOBR2iEo2lVjaYykH3ztIa5fWhfJMCwttfM7x49C+vZbsXL5cKI9SFKWAdEpwpJS+UsovU16vA9oC84CeUsoJhRBfoRMi+yOlhwTQXudUN6MmTfJWL6+MjIz46quv+O9//8vlbH6ahoWF0aVLFxo1asSxY8fw9/dn1apV+Pr6AtqO3i1btuTdd98lPDyc8PBwqlatmucY9uzZw4kTJ9i+fTu7du165v1bt27Rr18/vL29OXv2LHv37uXtt9/O8Z5Dhgxh3bp1REdHp5UFBQURHBzMkCFDcrzWz8+PV199lZMnTzJixAhCQkLo2bMnr732GsePH+ejjz5izJgxuX6uuLg4ZsyYQUBAAPv37+fBgwcMGzYs2/rbt2+ne/fudOrUiaNHjxIYGIiXlxfJKTs7xsfH4+fnx/Hjx9myZQuRkZFpLVGKfsTExzA5cDJuP7ix6tQqzI3NmdB2Ahc+vIB3Q2+dFuvbvHkzmzdvznP9rl3h/HmYOlXrxtq4EerXhzFjIMO3saIoxYGUstQcTZo0kdk5c+ZMluVar3rWx6JF6fUWLcq5bkaNG+etXl54e3vL1157TUop5UsvvST79u0rpZQyMDBQAjIiIkJKKeX48eNlrVq1ZFJSUtq1S5YskWZmZjImJkZKKaWXl5ccMWKETs9MPXdwcJCxsbGZ6mW839GjRyUgr127lufPFhUVJa2srOSiDP/Qw4cPl3Xr1s1Uz9XVVc6aNSvtHJAjR47MVGfcuHHPXPfll19KQF69elVK+ey/2ZIlSyQgz507l3bN8uXLpZmZmUxOTk6rY21tnfZ+q1at0v4b5MXZs2clIENDQ7Otk933ppJZYlKi9A/yl5VmV5JMQTIF2WdtH3ntft6/556Gtg1Nvq4NC5PS2zv9/+2ZM/MdhqIoWQCOyALkBDqvSy6EaCyE+EUIcSTlWCaEaKy/lKto5ZS2ZOya9/HJuW5GR4/mrZ6uZs6cydq1azl69Ogz7509e5YWLVpgZJT+n7RNmzbEx8dz6dKlgj0YcHd3x9zcPNv3PTw86NixI+7u7vTq1YuFCxemjRkKCQnBxsYm7Zg+fToAdnZ2vPnmm2ndVLGxsaxcuTLX1hsAT8/M+6+dO3eOpk2bZipr3rx5rvcxNzfHLXUEKVC5cmXi4+O5f/9+lvWPHTtGhw4dsnwPtBaoHj164Orqiq2tbVqcISEhucaiZG/n5Z00XtyYIZuGEP4onCaVmrB30F7W9F6T6zibnHTt2jVPA+qzUrkyLF0Khw5Bnz7w4Yfp72XTM6soShHSdaG/t4DDQCXgj5TDCTgkhBiYh+vLCSE2CiFihBDXhRADcqlvJoQ4K4S4oUucpVWzZs3o1atXnrpeMtJlUG12rK2tc3zf2NiYHTt2sGPHDl588UX8/f2pXbs2x48fp3LlygQHB6cdGbuAhgwZwsGDBzlz5gwbNmwgJiYGb2/vAseTVyYmmRfzTv23Su1y0kVMTAydO3fGysqKZcuWcfjwYbZv3w7kfSC0ktmpO6fosqIL/1n+H07cPoGLvQsreq7g0NBDtHVtW+D769pFlZWmTWHNGrC01M4fPAB3d+jeHc6cyflaRVEKj64tOF8CE6WUnaSUk1KO/wATgWl5uH4+EI+WFL0FLBRCNMih/mdA8Zg6VExMnz6dv//+O+0XZ6p69epx4MCBTL+Y//nnH8zMzKhZsyagzSJKKsT5rUIIWrZsyeTJkzl8+DCVK1dmzZo1mJiYUKtWrbSjXLlyade0bdsWNzc3/P398ff3p3v37jg6Our87Lp163LkyJFMZYcOHSrwZ3pao0aNshyDBForUmRkJNOnT6ddu3bUrVuXO3fu6D2G50H4w3B8Nvvg8V8Ptl/ajp25HTM7zuT8yPPFflPMo0e1dXM2b4YXXoD334dbtwwdlaI8f3T9KeEI/JpF+Vogx7m0QghroBdagvRISvkPsAnIciSqEKI6MBDI30IrpVStWrXw8fFh7ty5mcqHDx/OzZs3GT58OGfPnmXr1q2MGzeOkSNHpk2xrlatGocOHeLatWtERkbmq5UiOwcOHGDatGkcPnyYkJAQNm3aRGhoKPXr18/12sGDBxMQEEBgYGCeuqeyMmzYMC5fvszo0aM5f/48GzZsSFvfRB8tWKkmTJjA2rVr+fzzzzlz5gynT59mzpw5PH78GBcXF8zNzfnhhx+4cuUKW7duZeLEiXp79vMgJj6GL/Z8Qe15tfkx6EcEgpFNR3Lpw0uMaT0GCxMLQ4eYqw4d4NIl+OCD9MkKtWrBlCnw6JGho1OU54euCU4g8FIW5S8Bue3aUgdIlFJeyFB2HMiuBWceMJ5c1tcRQvikjgcqLuvEFLZJkyY907VSpUoVtm3bxrFjx2jYsCGDBw+mf//+aeNdAEaPHo2ZmRn169fH0dFRr+NC7O3t2bdvH127dqV27dp8+umnTJw4kYEDc+25xNvbm5iYGJydnencuXOu9bPi6urK+vXr2bRpEx4eHsyZM4fJkycD2jpC+vLqq6+yceNGtm3bRqNGjfDy8iIwMBAjIyMcHR35+eef+e2336hfvz5+fn58++23ent2aZaUnETAsQBqz6vN5N2TiUmIoYdbD04PP828V+fhaK17q15epC6ZoG9OTrBgAZw6BT16QEwM+PlB7956f5SiKNkQMpeRr0KInhlOKwFTgPXAgZSyFkBPYIqUckEO92kLrJVSVsxQNhR4S0r50lN13wB8pJRdhBAvAcullM65fRhPT0/5dDdFqrNnz1KvXr3cbqGUInPnzmXSpEk8ePCgUH6J6cvz/L0ppWTH5R2M+d8YTtw+AYBnZU9md5qNVzWvQn9+6vdFbj8HC+rvv7XdyqdOhU4pm9o8eaKtq1OMvzUVxaCEEEellJ6518yaSe5VWJdFmU/KkdE8INsEB21rB7unyuyAhxkLUrqyvgZezUNsipJm/vz5NG3aFEdHRw4cOMDUqVPTtrpQip+DNw4ybtc4dl/bDYCLvQszOsygn3u/IhtjU9iJTaq2bWH//szJzPvva5t4zpoFzZoVSRiK8lzJNcGRUurrJ80FwEQIUVtKeTGlzAM4/VS92kA14O+UX0xmgL0Q4hbQQkp5TU/xKKXMpUuXmD59Onfv3sXZ2Zlhw4YxadIkQ4elPOVc5DnG7xrPxnMbAShrURbfNr6MbDYSS1NLA0dXeDImNw8ewPbtEBGh7WLepw98+aU2VkdRFP3ItYtKrw8TYjXawlrvAQ3Rppm3klKezlDHBHDIcFkr4AegMRAhpcx2GpDqolJKoufle/NG9A2m7J7CkuAlJMtkLE0sGdViFGNaj6GMRZncb1DKREXBV1/Bd99ps66MjWHIEG2TT+dcO+QVpfQraBdVfhb6e00IsVcIESmEiBBC7BFC5LU7aThgCdwBVgEfSClPCyHaCiEeAUgpE6WUt1IP4B6QnHKu9vBVlBLm3pN7fLbjM2p9Xwv/Y/4IBMOaDOPSR5eY3mG6QZObbt260a1bN4M8294eZszQdiwfPFhbCHTxYqhbF+7eNUhIilKq5GUMThohxHto42xWAD+nFLcFNgohPpBSPrtzYgZSynvA61mU/w3YPHsFSCl3A3r5eyY5OTnTSr+KYmj6nKpf3MTExzD34Fy+3vc1UXFRAPRt0Jep7adSu3xtA0en2bJli6FDoGpV8PfXBiFPmgQ2NlC+vPaelNoMLJssfzoqipITnRIcYCzwiZTyhwxl/kKIo8A4IMcEx5Csra0JCwvDyckJU1NTNfBUMSgpJQkJCdy+fVtvqzIXF7GJsSw+upgZ/8zg1iNthbtONToxo8MMmlRuYuDoMtu0aZOhQ0hTty78+itkXItz2zZ45x0YNw5GjEhfLVlRlNzpNAZHCBEHNJBSXnqqvBZwWkqZ/WZFRSCnMTjJyclERkYSFRVFYmJiEUemKM8yMTHB3t4eBweHUtGyGJcYh/8xf6b/PZ2wh2GANuX7qw5f0aFG9vt3KdkbNgxS1qukcmWthWfwYDA1NWxcilIUCjoGR9cE5yLwrZRy4VPlw4FRUso6+Q1EH3JKcBRFKRwJSQksDV7KtL+nERKlLR7p4eTBF+2/oFudbqq1tACk1GZbTZgAx45pZTVqwOefw8CBKtFRSreiWAcno9nAvJTdw/9NKWuNtt3Ch9lepShKqZOYnMiy48uYuncqVx9cBaCBYwP8XvLjjXpvFOv9olItXrwYAB+fp5f1Kh6EgC5doHNnWL9em2F1/rzWihMdDf/3f4aOUFGKL52niaesMvwpkDqv9SwwS0r5u55j05lqwVGUwpeUnMTKkyv5Yu8XXLqn9VbXdajLFK8pvNngzRKR2KQqqpWM9SUxEVav1raB2L4d7FKWTj11CtzcVIuOUroUWQtOyvo0/wH2Sik35veBiqKUTPFJ8Sw/sZyv/vmKi/e0tTprlavFZK/J9Hfvj7GRsYEj1N3QoUMNHYJOTEy0rqmMW7w9fqxt8GllpXVlvfMOmJkZLkZFKS50HYMTC9QtrqsJqxYcRdG/JwlPCDgWwMx9MwmNDgWgepnqTPKaxMAXB2JipGtPt6JP585Bz55w9qx27uqqJTre3irRUUq2ol7o7zigFhNXlOfAo/hHzP53NtXnVmfktpGERodSz6Eey95YxoUPLzCo4SCV3BQDdevCyZOwahXUq6ftb+XjAzVrwpw5kJBg6AgVxTB0bcHpAnwFTAaOAjEZ309ZyM9gVAuOohTc/Sf3mXdoHnMPzuXeE+1/6UYVGzGh7YQSM3g4r27evAlA5cqVDRyJfiQlwbp1MG2aNi7nhRfg+HG1Y7lSMhX1NPGMy65mvFAAUkpp0E54leAoSv6FRYfx/cHvWXhkIQ/jHwLQqmorJrSdQJdaXUrldO+SNsg4r5KT4Y8/wNwcOnXSyq5ehblz4ZNPwMXFsPEpSl4U9TTx9vl9kKIoxdOJ2yf4Zv83rDy5ksRkbRHMDtU78Hm7z/Fy9SqViU2qSpUqGTqEQmFkBF27Zi6bNQsWLoT58+Gtt2DMGKhf3zDxKUpRyFOCI4SwAmah7SNlCvwP+EhKGVmIsSmKUkiklOy6uovZ/87mz8t/AmAkjOjToA+ftvyUZlWaGTjCopHaRfU8GDZM28F89Wr4+Wft6NoVPv4Y2rdX3VhK6ZOnLiohxCy0ncBXAE+AAcBuKeWbhRueblQXlaLkLCEpgV9P/8rs/bMJvhUMgJWpFUMaDWFUi1HUKFvDwBEqhe3KFZg9GwICIC5OK/P1henTDRuXojytSMbgCCEuAxOklKtTzpsB+wALKWVSjhcXIZXgKErWImIi+CnoJxYcWcCN6BsAOFk78WGzD/mg6QeUsyxn4AiVonbnjrbP1fz52nidxo218rNntd3MK1QwbHyKUlQJTjxQXUoZlqHsCVBHShma34frm0pwFCWzozePMu/QPFafWk1ckvbnel2HuoxuOZq3XnwLCxMLA0doWE2aaLubHz161MCRGE5CQuYVkL284OBBbTHB//s/bSaWohhCUQ0yNgbinypL1OF6RVGKSHxSPOvPrGfeoXnsv7EfAIHgtdqv8WGzD+lUs1OpmupdEEFBQYYOweAyJjdPnoC9PcTHg7+/drRrBx98oC0mqBYOVEqSvCYoAlguhIjLUGYB/CiEeJxaIKXsrs/gFEXJu/CH4Sw+upj/Hv0vtx7dAsDe3J7BjQYzoukIaparaeAIix/V4puZpSVs2gQXL2pTyn/+Gfbu1Y4KFeC336BlS0NHqSh5k9cuqiV5uZmU8t0CR1QAqotKed4kJSfx5+U/WXx0MVsubCEpZUhcA8cGjGw2koEvDsTGzMbAUSol1cOHsHy5Nr388mUIC4MyZbT3Ll2CGjW0KemKUhiKdKG/4k4lOMrzIjQqlIBjAfgf80/bH8rEyIRudboxstlI2ldrX6rXr1GKlpTaQoE1UibZxcVB1apgawtDh2obfJaSxaCVYqSoF/orECFEOcAfbVfySMBXSrkyi3qfAd6Aa0q9BVLKWUUZq6IUN4nJifxx8Q8WH13MtkvbSJbawuI1y9bkvcbvMajhICraVDRwlCXLlClTMn1VsiZEenID2lRzKyvtq6+vtrnnK6/A4MHQrZsaq6MUD0XagiOEWIW2wecQoCGwFWglpTz9VL0xaIsJngBqAjuAsanT1LOjWnCU0ujUnVP8cvwXlp9YTvijcABMjUzpWa8nQxsPpX319iVq0PCUKVNYt24dp06dyrXutWvXqF69OocPH8bTM99/yGUrp60aqlWrxsiRIxk9erTen6sPI0eO5NSpU+zevdsgz09Kgj//1NbT2bQpfVNPBwcICtJaeBSlIEpMC44QwhroBbhLKR8B/wghNgFvA+My1pVSfp3h9LwQ4negNZBjgqMopcWdmDusOrmKX078QlB4+kyfOuXr4NPYh3c83sHR2lFvzxs0aBA///wzACYmJpQtW5YGDRrQu3dvfHx8MM041aaARo8ezYcffpinulWrViU8PBwHBwe9PT+jyZMnF8p9nwfGxvDqq9oREQErVmjJTlISODun19uwQZuJVUj/CRUlW0XZRVUHSJRSXshQdhzwyukiof2J1RZYlM37PoAPgIvaQU4pwWITY9l8fjO/nPiFbRe3pQ0YLmNRhn4N+vGOxzu0cG5RaGNrOnbsyLJly0hKSiIiIoK//vqLyZMns2zZMnbt2oW1tbVenmNjY4ONTd4GPhsbG1OxYuF1uz3vXVMJCQl6SV4dHWHUKG3dnHv30rd9uHIFevUCExPo3BkGDIAePUBP30qKkqOibNe2AaKfKosCbHO5bgpanFnO5JJSLpZSekopPR0d9fcXraIUhYSkBLZf2s67v79LxdkV6bOuD1subEEIQbc63Vj35jrCPw1nYdeFtKzaslAHDpubm1OxYkWqVKlCw4YN+eSTT9i9ezdBQUF8/XV6o2p8fDxjx47F2dkZKysrmjZtyp9//pnpXufOnaN79+7Y29tjY2NDy5YtOXnyJKAlFe7u7ml1T548SYcOHbCzs8PGxgYPDw8CAwMBrYtKCJFpOvfevXtp3rw5FhYWODk58fHHHxMfn75M10svvcTw4cMZP348Dg4OVKhQgdGjR5OcnKzzv8mjR48YOHAgNjY2VKxYkdmzZ2d6PyQkhDfeeANbW1tsbW3p2bMnN27cSHv/6c8KsHTp0kwJXmqd1atXU7NmTWxtbXn99deJjEzf6i8pKYnRo0dTtmxZypYty6hRo0hKyryI/Pbt22nbti1ly5alXLlydO7cmbNnz6a9n/pvuWrVKl5++WUsLS1ZsGABdnZ2rFu3LtO9du7ciVmwrUkAAB+LSURBVKmpKbdv39bp30sIbRXkVA8famNzpIStW7VNPitU0L5u3ZreraUohaEoE5xHgN1TZXbAw+wuEEKMBN4BXpNSxmVXT1FKksTkRP535X8M3TSUit9UpMuKLiwNXkpUXBSNKzVm7itzCfskjE39N9Grfi+Drjbs7u7OK6+8wvr169PK3n33Xfbs2cPKlSs5deoU3t7edOvWjePHjwPaBpZt2rRBCMHOnTsJCgpixIgRz/xCTjVgwAAqVarEoUOHCA4OZsqUKVhYZP2Zw8LC6NKlC40aNeLYsWP4+/uzatUqfH19M9VbsWIFJiYm/Pvvv/zwww989913rFmz5pn7HT16NMdVjL/99lvq1atHUFAQfn5+jB8/ng0bNgCQnJxMjx49uH37NoGBgQQGBnLz5k1ef/31LMf05OTatWusWbOGjRs3smPHDo4dO8aECRPS3v/mm2/48ccfWbRoEfv37ycpKYkVK1ZkukdMTAyjRo3i0KFD7N69G3t7e7p165Yp+QPw9fVl+PDhnDlzhl69etG/f38CAgIy1QkICKBr1644OTnp9Dme5uEB27bBzZswb562hs7jx7Bypday8+RJet1SNKFXKS6klEVyANZoqyHXzlD2C/BVNvUHAzeAGnl9RpMmTaSiFEeJSYky8Gqg/GDLB9Lxa0fJFNKOBvMbyC92fyHPRZwzWHze3t7ytddey/K9sWPHSktLSymllJcuXZJCCHn9+vVMdXr06CE/+OADKaWU48ePly4uLjIuLi7L+02ePFk2aNAg7dzW1lYuXbo0y7pXr16VgDx8+HDavWvVqiWTkpLS6ixZskSamZnJmJgYKaWUXl5eskWLFpnu07FjRzlkyJBn7g9I7cfgs1xdXWXHjh0zlQ0ZMkS2bt1aSinljh07pJGRkbx69Wra+5cvX5ZCCLlz584sP2tqvNbW1pn+PczNzeWDBw/SyqZNmyZr1qyZdl6pUiU5bdq0tPOkpCRZu3Zt6eXllWXsUkr56NH/t3fn4VVV5+LHv29IICSBJECIQSHMAhFQQRFFARV/2KponbC0Fx+LE+JQlMp1qGjrUIefem2tWGvFem3l9tpS1OJTh6CoKIPKJKAMMoRgCCGQkIGY9/6x9klOTk6SE5Kc5Jy8n+dZz9ln73X2XllZSd6svfZaRRoTE6MffvihqlbX5eOPP14j34oVK7RDhw66a9cuVVXdv3+/xsfH6+LFi+s8d1Ns2aL64IOqc+ZU7ysrUz3+eNXrrlN9+23V8vIWubSJMMBKbULcEbYxOKpaLCKvAw+IyAzcU1RTgNMD84rINOAhYKKqbg1XGY1pTiVHSnhn6zss2rSIf276J3mH86qODe4+mCuzruTKrCvJ6pnViqVsmKpW3RpbvXo1qsqwYcNq5CkrK+Pss88G4PPPP2fcuHF0DPFZ4dmzZzNjxgwWLFjAOeecw6WXXsqQIUOC5v3qq6847bTTiPGbXW7cuHGUl5fzzTffMGLECICqV59evXrx3Xff1Trfyb4VJuswNmDa3rFjx1b14Hz11Vf06tWLvn37Vh3v378/vXr1YsOGDZx77rn1nttfZmYmycnJQctbWFjInj17apQlJiaGMWPGsHNn9VKAW7Zs4d577+XTTz8lLy+PyspKKisr2bFjR41rBT6NNnr0aIYPH86CBQu46667ePXVV+nWrRvnn39+yOVvjP794a67au5btgw2bXLp+echNRUuusj18kyaBHV06BlTr3CvJTUTeBH4DsgHblTV9SJyJvAvVfXdmP410B1Y4Tfm4BVVvSHM5TWmUfIP5/Pm12/yj43/4O0tb3P4SNVKJvRP7c8Vw67gyhOuZGT6yIiZiG/Dhg309yZBqaysRERYsWJFrcGpnTt3Pqrzz5s3j2nTpvGvf/2Lt99+m/vvv5/nnnuOa665plHn8a/PwLKJSNAxOC21yKavLDExMbVuVx0JMvAk1PLW54ILLuC4445j/vz5HHvsscTGxjJs2LBat6iCDRafMWMGTz/9NHfddRcvvvgi06dPp0OHDo26flNMnAhffAH/+78ubdjglolYsACSktwK5/5PZhkTirAGOKq6H7g4yP4PcYOQfe/7hbNcxhwtVWVz/mbe+votFm1axLIdy6qefgIYlTGKKcdP4eIhF3NCzxMiJqjxWbduHUuWLOGee+4B4KSTTkJVyc3NZeLEiUE/c9JJJ/HKK69QXl4eci/OoEGDGDRoELfccgs33ngjL7zwQtAAZ+jQoSxcuJDKysqqXpxly5bRsWNHBgxo/rW2li9fXuv90KFDq8qSk5PD9u3bq3pxtm7dSk5OTlUPV1paGnv37q3RC/bFF180qgzJyclkZGSwfPnyql4yVeWzzz4jIyMDgPz8fDZu3Mizzz5b9X1ZvXo1FRUVIV1j2rRpzJkzh9/+9resXr2av/41vDNyiLjxOiNHwgMPwMaNLtB5/XU4eBCOPbY677XXwsCB8MMfQlZW9RNbxgSy1cCNaaSi8iLe2/YeS75ZwpJvlrDtwLaqY7ExsUzqN4kpx0/houMvondy5Mx2VlZWRm5uLpWVleTl5fHuu+/y0EMPMWrUqKrJ7gYPHsy0adO4+uqreeKJJzj55JPZv38/2dnZ9O/fnx/96EfMnDmT5557jiuuuIK7776b1NRUVqxYwdChQznxxBNrXLOkpIQ77riDyy+/nL59+7J3716WLVvGmDFjgpZx5syZPPXUU8ycOZNbb72VrVu3MnfuXGbNmkVCQkKz18ny5ct5+OGHueyyy8jOzubll1+uGtx77rnnMmLECKZNm8bTTz8NwM0338zJJ59cFYhMmDCB/fv389BDDzF16lSys7NrPbEUiltvvZWHH36YwYMHM3z4cJ599ln27NlTFeCkpqbSo0cP/vCHP9C7d292797NnDlziI0N7Vd8SkoKl19+ObfffjtnnXUWgwYNanQZm9OQIW525Lvvdk9i+YKYnBx44QW3PXcuZGbCBRe4NH68WyzUmCpNGcDT1pINMjYtobKyUtfuXauPffSYnr3gbI17IK7GIOHuv+muV/3tKn11zataUFLQ2sU9KtOnT68acNuhQwft3r27jh8/Xp955plag4XLy8v1vvvu0379+mlcXJymp6frhRdeqCtXrqzKs27dOj3//PM1MTFRk5KSdOzYsbp27VpVrTnwtqysTK+66irNzMzUjh07akZGhl577bVaWFioqrUHGauqLl26VE899VTt2LGj9uzZU2+77TYtLS2tOj5+/Hi96aaban19wQZRZ2RkaEZGRtA6yczM1Pvuu0+nTp2qiYmJ2rNnT33kkUdq5Pn22291ypQpmpSUpElJSXrxxRfrzp07a+R57rnntE+fPpqQkKBXXnmlPvXUU7UGGTc0EPnIkSN62223aXJysiYnJ+usWbP0hhtuqDHI+N1339WsrCzt1KmTZmVl6ZIlSzQxMVH/9Kc/1VmX/pYuXaqALliwIOjxtqC4WPVvf1O9+mrVtDRV9+yVS/HxqsuWtXYJTXOiiYOMbbFNY4LYVrCN97a9x/vb3+e9be9VLZEAIAhjjhvD+QPPZ/LAyYzKGEWHmPCNVzDNp76lGtqb1157jeuvv56cnJwW6Q1rbpWVsGKFm0/njTdg3To3o7JvrPbNN7v3kya5ZPPARh5bTdyPBTjmaO06uIv3t71fFdB8W/htjePpielMHjiZyQMnM6n/JLondK/jTCaS5OTkAO6ppfbq8OHD5Obmcskll3Deeefx2GORua7xgQOQkuK2KyvhmGNcgOMzaBBMmOCWjTjnHPDu7pk2zAIcPxbgmFCoKt/s/4aPdn7ERzs+4oMdH7A5f3ONPKnxqUzoO4Gz+53NxL4TGZY2LOIGCBsTinnz5vHggw8ybtw4Fi1aRNeugfOxRh5V2LwZ3nkH/v1veP99N1jZ55FH4M473XZODhQXu4HL9iPetliA48cCHBNMWUUZq/as4qMdH/HRzo/4eOfHNeakAejSsQtnZZ5VFdCMPGZkRK3QbYypW0UFrFoFH3zg0n33gW86oF/9Cn75S9ejc+aZbrblMWPgpJNs/p3WFjGriRsTDqrK1oKtrMhZwcqclXyy6xNW5qyk/Puac4H0TOzJGb3P4IzeZzCuzzhG9RpFbIz9OISqosItoBjprrvuOgCef/75Vi6JaUmxsS5oGTMG5sypfTwtDfbsgYULXQKIi3OTDfo/9KZqvTyRxHpwTMRSVXYd3MXKnJVVAc3KnJUUlBbUypuVluUCmj5ncHrv0xmQOsBuOYVIFb79Fj75BJYuhexs2LIFFi2CH/ygtUvXNDbI2IBr45s2wYcfwqefurR+PUyd6tbNAti3D4YNg1NPhVGj4OSTXS9P794W9LQU68Ex7cL3ld/z9f6vWbN3DWv2ruGL3C9YmbOSvcW1VzvumdiTU3qdwuheozn12FMZe9xYUjuntkKpI1NxMaxcCR9/7MYvrFrlVn2OjXVzkoCbb8QbnxvR5s+f39pFMG2AiJt7Z8gQN5EguDE7/uN2Vqxwg5bffNMln+7dXaAzf75bhsK0HRbgmDYn/3B+VSCzZu8a1ny3hnXfraO0orRW3tT4VEb3Gl2VTul1Csd1Pc56Z0KkCt9843pnsrPd+IQdO1wAU1LiAptgoqV6fbeojAnUtatLPpMnw9atrnfn889dWr0a8vPdYOZUv/+hpk93P1dZWXDCCS5lZUHPntHzsxMJ7BaVaRWqSm5RLhv3beSrfV9VvW7I20DOoeBdA32S+zAifQQj00cyIn0EozJG0T+1vwUzR+HRR2HxYvdLGtwv3aKi0D8fHw+lpe4/10jWtSu88oqtc2SOjirs3OnWzpo8uXp/v36wfXvt/D16wK23grfyCaWlrse0u806EZTdojJtWmlFKdsKtrE5f3ONYGbjvo0UlhUG/UxCXALDew5nRPqIqoBmePpwUuJTwlz66PXpp7B2LZSVud4a362nUPmWOPIFSJFrMQsXwuzZF7Z2QUwEEnETCAZOIuj7+Vq/3k1AuG6d2963D2L8Hs5cutQFRt26weDBtVNWVnQM5m8t1oNjmqygpIAtBVvYsn9LzdeCLew+uBsleBtLiU9haI+hDO0xlCE9hjA0zb32S+lnMwOHge+/z+XL3e2p7GzXrd65swt8ysrq/mxCAjz9NMyYEa7StgwbZGzCRRV27YJOndytKoA//xlmzqy79/TgQejSxW0/84zr8enXrzqlpkb3LS/rwTEtSlXJL8lnR+GOGmnnwZ1sLdjKlv1bgj615NNBOpCZksnAbgNrBTNpCWl2e6kV+f/3ecUVbl9ZmeuV+eQTN67g00/dL99OnVwvT7TFARdccEFrF8G0EyLuiSt/P/0p/OQnkJvrJibcvNk9zbV5MxQUVAc3AE8+Cdu21fx8167Qty9cf70LlAAKC90/Lr17u+Pt+VesBTjtmC942XNoD3uK9rDr4C52Fu50QcxBL5Ap3ElJRUm950mIS2BA6gAGdBvgXv22+yT3Ia5DXJi+ItNUnTrBaae59POfu305OS7Q+eADeO892LjRBULRMAna4sWLW7sIpp0TcZMMZmS4FdHrMnu262Hdtq06HTwIa9a4oMYnOxsuvthtJyW58WX+6c473X5w438SEqI3CLJbVFGoorKCvOI89hTtqQpeql79tnOLcmtNgBdMSnwKfZL70Ltrb/ok96lKmcmZDOg2gPTEdOuJaUeOHHFBTlZWzfEExpjwUXVPcG3fDunp1b1Df/87zJ3rbocdPlz7cyUl1f+cjB8Pn30Gxx7r1u465hh3rmOOcTM6n3uuy1dR4X7uO3cOy5dWxW5RtQPF5cXkHc5j3+F95BXnBd8+nFf1/kDpgZDPndwpmYwuGfTq0oteXXqRmZxZFcD07tqb3sm96dop8temMc0nLg6GD2/tUhjTvom4p7J69Ki5/5JLXFJ1PTu7dlWnvLyaPa+FhW5cz5YtLvm76abqAGfVKter27VrdQCUnl59/Vmz3HtwAVdFhdufnNy6vUMW4ISBqlJ8pJiCkgIOlB6goLSg7u1Sb7ukoOpYQ7eIAsVIDN07dyejSwYZSRnVr/7b3mvnuDCH5Ma0ITbI2EQrEbe6ekqKm4cnmC++cGPrdu+GvXvdWCDf69ix1fkKC90/Nr7JD7/+uuZ5rrmmenvOnOrlLTp0cE+Ide/uAp6zzoIHH3THSkvhhReqy5iaWr2dkuJunTWVBTh1qKisoLi8mEPlhzhUdii01zqOFZYVUlFZcdRliY+NJy0hjbTENHok9CAtofrVf59vOzU+1Z5CMsYY06AuXapnca7Leee5cXcFBTWDoPx8l3y9N+ACmb593f5Dh1yvUV5e9TGfffvg5pvrvuaiRU36soAoC3AOlh3k9a9e5/CRw7VSyZESt11Rx/6AdKSyjilcj1Ln2M6kdk4lNT6V1M6ppMSnuO14bzvYMW87MS7RxrgY0wKs58aY0Ii43phu3dyaXHX5/e+rt8vLq4Og/Pzqwc0AHTu6J78KCuDAgdoppRmmPQvrIGMR6Qb8ETgP2Af8p6q+GiSfAI8Avlk2XgDmagOFlV6iXN9MhVWB8kQyunehS6cudOkY5NVve/asLlDWBcprv5YeSKZTbKd6L1df/BLqt6g5znHMMS46D5Se7iL2lv58NGkr39OmnqMtlKE5ztEWfj6a6xzGRDtViIlp2iDjcAc4fwFigJ8BJwJvAqer6vqAfNcDs4FzAAX+DfyXqj5X3/mT+yfr2Q+fTUJcAgmxCe41LoHOcZ2rtgNT59jOnH5KAhwJSN93BCSifvm2hXM0RxmiRVv4fjTHOdpCGZrjHG2hDM11DmPag6Y+RRW2AEdEEoEC4ARV3ezt+zOwW1XnBuT9GHhJVZ/33v8MuFZVT6vvGkf7mHhb+KXVFsrQHOewX97V2sL3oznO0RbK0BznCP75C73PhzYfTlv4OoxpLyLpMfHBQIUvuPF8CQSb2ijLO+afLyvYSUXkOuA6gD6BC4IYY0y93mjtAhhjWkg4p+lKAg4G7CsEutSRtzAgX5IEGWmrqs+r6mhVHZ2WltZshTXGtAf/9JIxJtqEswenCAicMa4rEGwd48C8XYGihgYZG2NM49gq4sZEq3AGOJuBWBEZpKq+aYJGAuuD5F3vHfusgXw1rFq1qkhENjW+aKNG1XVEZNWq8JyjLZQBYORIiA3SLioqRL78svb+5v58NGkr39NoaZtt4etojvbd5n5GeuCeajXNw+qz+RzflA+HLcBR1WIReR14QERm4J6imgKcHiT7y8BsEXkL9xTV7cAzIVxmU1MGJJmaRGSl1WfzsLpsXlafzcfqsnlZfTYfEWnS4pLhXipvJtAZ+A74C3Cjqq4XkTNFpMgv33xgMbAWWId7nHx+mMtqjDHGmAgV1pmMVXU/cHGQ/R/iBhb73ivwCy8ZY4wxxjRKuHtwWtrzrV2AKGP12XysLpuX1WfzsbpsXlafzadJdRnWmYyNMcYYY8Ih2npwjDHGGGMswDHGGGNM9LEAxxhjjDFRJ+ICHBHpJiJ/F5FiEflWRH5cRz4Rkd+ISL6XfhNsqYf2rBF1OU9EjohIkV/qH+7ytmUiMktEVopImYi81EDen4tIrogcFJEXRaRTmIoZMUKtTxG5WkS+D2ibE8JX0rZPRDqJyB+9n/FDIvKFiJxfT35rn3VoTF1a2wyNiLwiInu89rbZmyevrryNapsRF+AAvwPKgXRgGvB7EQm2EOd1uEfSRwIjcHOyXx+uQkaIUOsS4DVVTfJLW8NWysiQA/waeLG+TCLy/4C5wDlAJtAfuL/FSxd5QqpPzycBbTO7ZYsWcWKBnbiFjZOBe4CFItI3MKO1zwaFXJcea5sNexjoq6pdgYuAX4tIrVnHj6ZtRlSAIyKJwKXAvapapKrLcCvl/TRI9unAE6q6S1V3A08AV4etsG1cI+vSNEBVX1fVfwD5DWSdDvxRVderagHwK6xd1tKI+jQNUNViVZ2nqttVtVJV3wC2AcGWrrD2WY9G1qUJgdfWynxvvTQgSNZGt82ICnCAwUCFqm722/clEKzXIcs71lC+9qoxdQlwoYjsF5H1InJjyxcvagVrl+ki0r2VyhMNThKRfV739r0iEtYJTCONiKTjfv6Dre9n7bMRGqhLsLYZEhF5VkQOAxuBPcBbQbI1um1GWoCTBBwM2FcIdKkjb2FAviQbh1OlMXW5EBgKpAHXAr8UkatatnhRK1i7hOD1bhr2AXAC0BPXI3kVMKdVS9SGiUgc8N/AAlXdGCSLtc8QhVCX1jZDpKozcW3sTOB1oCxItka3zUgLcIqArgH7ugKHQsjbFShSm9nQJ+S6VNUNqpqjqt+r6sfA08BlYShjNArWLiF4GzYNUNWtqrrNu12wFngAa5tBiUgM8GfcuLtZdWSz9hmCUOrS2mbjeH9flgHHAcHuEjS6bUZagLMZiBWRQX77RhK8e3C9d6yhfO1VY+oykALWE3Z0grXLvapqY02ah7XNILye6z/iHii4VFWP1JHV2mcDGlGXgaxthiaW4GNwGt02IyrAUdViXPfVAyKSKCJnAFNwkXSgl4HZInKsiPQCbgdeClth27jG1KWITBGRVO/R+1OBW4BF4S1x2yYisSISD3QAOohIfB33218GfiYiw0QkBfcUxkthLGpECLU+ReR8bxwEIjIEuBdrm8H8Hneb+UJVLaknn7XPhoVUl9Y2GyYiPUVkqogkiUgH70mpq4B3g2RvfNtU1YhKQDfgH0AxsAP4sbf/TNwtKF8+AR4F9nvpUby1tyw1ui7/gnuapQg3COyW1i57W0vAPKqfAPCleUAfr976+OWdDezFjYH6E9Cptcvf1lKo9Qk87tVlMbAVdxsgrrXL35YS7pFaBUq9uvOladY+W64urW2GVJ9pwFLggNfe1gLXesea3DZtsU1jjDHGRJ2IukVljDHGGBMKC3CMMcYYE3UswDHGGGNM1LEAxxhjjDFRxwIcY4wxxkQdC3CMMcYYE3UswDHGNBsRuVpEisJ5PhG5Q0S2N5Cnr4ioiIw+ijKkisheEQk2u2qzEJFOIrLjaMpnjAnOAhxjooyIvOT9MVcROSIiW0XkcRFJbOQ53mjJcoboNaB/Yz7QAmW/C3hLVbc04zlrUNUy4DHgNy11DWPaGwtwjIlO7wAZuODgHmAmbmbViKKqJar6XWtdX0QSgBm4tYda2n8D40QkKwzXMibqWYBjTHQqU9VcVd2pqq/i/nhe7DvorefypogcEpHvROQvInKMd2weMB34oV9P0ATv2CMisklESkRku4g86q0ZFRLv80v83s/wzj/Vb98yEbnH2651i0pEfiEiuSJSJCIvA0l+x+osuydTRP4tIodFZIOITGqgyD/ATc3/UUAZhojIP0Wk0CvHJyIy3Dv2koi8ISJ3euUs9L7uGBGZ59V3rojc6X9OVd3vXeeqBspkjAmBBTjGtA8lQByAiGQAHwDrgFOBc3FBwiIRicH19CykuhcoA/jYO08xcA1uscGZwFTg7kaUIxs4w2/hzAnAPu/V12NyipevFhG5Avg1cB9wMrAJtz6NT31lB3gQ+C/cSsQrgL+KSBJ1OxNYpX5r2niL9y7DBT6TvHL8DrcwqM9ZQD/v67oB+AXwFtAJGIdbV+sRERkVcL3PgPH1lMcYE6Jgqx0bY6KItwL8j6leofdG4EtVvdMvz3/gFqUdraqfiUgJXi+Q/7lU9Vd+b7eLyEPAHbiVkkOxDIjHBTGf4P6YP44LmgBOBypwf+iDuQ1YoKrzvfcPishEYKBXvqJgZRcR3+aTqrrY23cX8B/AiV65gskEcgL23YQL9C5X1XJv3+aAPIXATar6PbBRRG4HMlR1si+/iMwFJgKr/D6XA/StoyzGmEawHhxjotNk79ZJKS6Q+AC42Ts2CjjLO17k3QLa6R2r90khEbnMu4WU633uSdyqvyFR1SLcH/QJIjIQSMb1fvTxepYmAJ/4BQ6Bhnpfj7/A9/VZ47ftC1x61pO/M27laH8nAcvqKSPABi+48dmL6zEjYF/gtUu8axpjmsh6cIyJTh8A1wFHgBxVPeJ3LAZ4E9fzEmhvXScUkdOAvwL3Az8HDgAX0fjBy9m4nos84EOv1+VTb98EYEndH22yqnpQVfV6dur7R28fkNqU6/guV8e+wGt3w9WLMaaJLMAxJjodVtVv6ji2GrgC+DYg8PFXTs0xJQBnALv9b1OJSOZRlC0b15tUQPVYm2zgh7hbV3Pr+exXwGnAi377TgvIE6zsR+tz4Oog+34iIh0b6MU5Gifgvj/GmCayW1TGtD+/w90aek1ExohIfxE5V0SeF5EuXp7twAkicryI9BCRONw4k2NFZJr3mRs5uid+lgEdgR8B73v7snFBV33jbwCeBqaLyLUiMkhE/hMYE5AnWNmP1tvAUBHp7rfvWdyg7IUicoqIDBSRq0TkxCZcx+dMWrYHy5h2wwIcY9oZVc3B9cZU4v6YrscFPWVeAvgDrrdkJe6WyRne4NzHgKdwY1kmAb88iuv7xuEU43pDAJYD31P/+BtU9TXcE0gPep8dDvz/gGy1yt7YMvpdby0u4Jrqt2837impjrgA7XNcj1TF0V4HQETG4gLPvzXlPMYYR/yefjTGGBNARCbjeo6GBQwcbu7r/A/wuao+1FLXMKY9sR4cY4yph6ouwfVwHddS1xCRTrhesSdb6hrGtDfWg2OMMcaYqGM9OMYYY4yJOhbgGGOMMSbqWIBjjDHGmKhjAY4xxhhjoo4FOMYYY4yJOhbgGGOMMSbq/B8q+OKdKoNS+AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1085d1908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "decision_boundary = X_new[y_proba[:, 1] >= 0.5][0]\n",
    "\n",
    "plt.figure(figsize=(8, 3))\n",
    "plt.plot(X[y==0], y[y==0], \"bs\")\n",
    "plt.plot(X[y==1], y[y==1], \"g^\")\n",
    "plt.plot([decision_boundary, decision_boundary], [-1, 2], \"k:\", linewidth=2)\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris-Virginica\")\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris-Virginica\")\n",
    "plt.text(decision_boundary+0.02, 0.15, \"Decision  boundary\", fontsize=14, color=\"k\", ha=\"center\")\n",
    "plt.arrow(decision_boundary, 0.08, -0.3, 0, head_width=0.05, head_length=0.1, fc='b', ec='b')\n",
    "plt.arrow(decision_boundary, 0.92, 0.3, 0, head_width=0.05, head_length=0.1, fc='g', ec='g')\n",
    "plt.xlabel(\"Petal width (cm)\", fontsize=14)\n",
    "plt.ylabel(\"Probability\", fontsize=14)\n",
    "plt.legend(loc=\"center left\", fontsize=14)\n",
    "plt.axis([0, 3, -0.02, 1.02])\n",
    "save_fig(\"logistic_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.61561562])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decision_boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.predict([[1.7], [1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_regression_contour_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fc318d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int)\n",
    "\n",
    "log_reg = LogisticRegression(C=10**10, random_state=42)\n",
    "log_reg.fit(X, y)\n",
    "\n",
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(2.9, 7, 500).reshape(-1, 1),\n",
    "        np.linspace(0.8, 2.7, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"bs\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"g^\")\n",
    "\n",
    "zz = y_proba[:, 1].reshape(x0.shape)\n",
    "contour = plt.contour(x0, x1, zz, cmap=plt.cm.brg)\n",
    "\n",
    "\n",
    "left_right = np.array([2.9, 7])\n",
    "boundary = -(log_reg.coef_[0][0] * left_right + log_reg.intercept_[0]) / log_reg.coef_[0][1]\n",
    "\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.plot(left_right, boundary, \"k--\", linewidth=3)\n",
    "plt.text(3.5, 1.5, \"Not Iris-Virginica\", fontsize=14, color=\"b\", ha=\"center\")\n",
    "plt.text(6.5, 2.3, \"Iris-Virginica\", fontsize=14, color=\"g\", ha=\"center\")\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.axis([2.9, 7, 0.8, 2.7])\n",
    "save_fig(\"logistic_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=10, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='multinomial',\n",
       "          n_jobs=1, penalty='l2', random_state=42, solver='lbfgs',\n",
       "          tol=0.0001, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = iris[\"target\"]\n",
    "\n",
    "softmax_reg = LogisticRegression(multi_class=\"multinomial\",solver=\"lbfgs\", C=10, random_state=42)\n",
    "softmax_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure softmax_regression_contour_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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+2vcnv/YA/hIgSyk/BD4E20Ehjb1eRVHOL++wBaGBf5SuQeP4bFtDm4UvApA9ZCL5fYZRHRRx3n7CVINzdipu6ftxS03E/dAuvJ9OB8Ds70zZNRGUXteG0qERWL3P/xCh3kcQOlVPyBTJ8fWSY7MtZL1he/neqBHygA7PKx17qC+iaxH3ztvIuFe28+P7sfz8cXt2rgynTfd8rn14nzrOWlEU5SJyQapYSCktwEYhxO3A/cA7ZzQpAzxP+/7k1+qepKI0EiFsnyetjRCTFWZY8ArV0BvrvxXqt3kVkQv+Q2nbLqTc/QomnyC7+0qDkcrWMVS2jiG//0gADMV5eCT9gde+zXiu3Iz350lIvUb5wDBKRralZEQU5uBzl2QTmsB7sMB7sEZVuiRnjoWceRYKl1tx6SAIeUBHwG0aOnf7f2/vkEpGv7CTG59OYNNnUXw/syMfThzAV09XMPiB/Vx5z0HcfWvsHk9RFEVpfBe6DrIeWw7ymfYCXU77vguQc2Z6haIo9Xcy99hqbfj9/eKjVrxD67977Jq+n4jPXqYk9jIOTpvtUHBcF5N3AIW9ryd10ovsfv0H9j8xl+yr70C/RxA65WdiIubS5ppl+Hy0B11B5XnHc44QRLyip2eqkeiP9WjOkDLF9lBf6j/NVB127AaW0cXClXcn80rCtzy6ci1hccUsfbYHj0aN4dOHe5N90PP8gyiKoihNotl2kIUQgcAgYBVQCQwGbj3xOtOnwHwhxGfAUeDfwPzmWamitAwny7udLPfWEKU5Vvwj6xcgS4uVNp/+F7OHL4fvfgVpaPw6ymg6yqPiKY+KJ2vkQzgfSyHQ8iZeS5IJe/AnQqf+Qum14RSPj6H0xiikS91vjZqz7ejqgDs0yrba0i+yZ1s49q4Fn+s0Qh7S4XW1/ekXpx9nfSTRmzXvxrFhbjvWfxBLl+uPMPSRvSpPWVEUpZk1Z4qFxJZO8QG2net0YJqUcoUQIhzYB8RJKTOklN8LIV4HfsL2MN/XwPPNuFZF+ds7Wd6tMQLk8kIrEb3q93ZS/OVeXLMOcfie17C4ezd4LeclBFWhbcngfXhE4pJ5kMDKGXh/dRDP79KweBo5Pjqa4js7UNE3hLoiUyEEHpcLPC7XqHlNkv2RhZyPLOy73opLjCDkIR0Bt2vo3Oy/vq07F3PXh5sY8+IO1n8Qw/o5sUy/ZijhXQoYMnUfvcelqTxlRVGUZtBsKRZSyjwp5UAppbeU0lNK2VlK+dGJn2VIKd2llBmntX9LShl0ou0kdUiIojQuvb7xAuSKIiuuPvV7O8l/ZyuVwZEUdRvU4HU4TAgqW8eQ3v5DkpInkPr9SEpGROH1VTJRV31Nu46L8J++Df3RsnMOYwwVhD+vp8dhI9Fz9WjuJ9IvImtIe9JMVZpj6RdeQVXc9PxuZhxeyqQPNmGu0fHR5Cv4Z7vRrHytM2WFxob81oqiKMp5XOgcZEVRLpCTKRZmc8MCZItJYqoEZw/Hx6nam0vljmPkDRjdOAWZG6BqwSQK0v7N4X6LSDoymcyPB2MOcSX42c3ERM0nfORKPFakgLnuHVzNSRB4u474TQY6/WzAe7DG0Xcs7Iit4cA4E8d/tSKl/cGy0cXCwMnJvLxrOY+uWEdYx2K+fq67LU95Sm+ykz0a41dXFEVRznBBqlgoinLhaZotzaKhAXJ1uS3gc3KgksNJJSsPAlDUY3CD1tDYKr66hwog+zbwnPM2PvP34b3wAJ5jVmMKcaNoQgeKJnfE1Kb2B+mEEHj2FXj21ag+Isl+30LOXAuF31px62pLv/C/2f7DR4SA+KFZxA/NsuUpvxPHhnnt+OnDGLpcn8mQaSpPWVEUpTGpHWRFacH0eitmc8PeBkyVtgDZ6Op4dFb2UyrO8UGYvPwbtIamVLJhKjkv9SXp8ETSl95AZbcAAl7fTvuYBUTcuPy8u8pOrW3VL3qk2I60tlbDobvNbI+u4chLZmpyHUu/aN25mLs+2sSMw0u58ekEDm8NYPo1Q/nP5cPY9FkU5hr1tq4oitJQagdZUVowg0E2OAfZZDv9Gb0DRzGDrXpFxe9Z+Ezo2qD5T6fVlOCesxnXgp0Yy9LR1RxHWE1InRNmJ19MLsHUeLShyiuGKp8OWPWudo1bNXeC7b9A6bcLMGSU4jNvLz7z9hExZjWmVu4UTu5I0eQ4zKHutY6hc/3zSOvjP0qOvmPhyAsWMl+z4H+LRugUHW5d7A9uvYKqGPWfXQx7MpFNi6P4YWYcH066gq/+1cNWT/luVU9ZURSlvlSArCgtmF4vqWngjqO52rYDqnfwubHqgwVYy0249ggBU4OWgGveNoJ3v4Z3xio0i+15XrOTL2YnP6SmR7NUoasuQl9TfKqPFBpVXjGUB/SiLKgfpSEDqfZqX2fVipOq5k6wBcqtIffQPDxWp+L74R6CXthK4Mu/UzKiLYX3daZ8YFitYwnx5+EjlUlWjr1nIfdTK3mfWvG8UhD6sA6f6zWEHcdjw4l6ynclM2BSMnvWhPH9zDiW/rsHK16J54oJh7nmoX0Et1NnLCmKojhCBciK0oIZjVZMpoY/pAegMzg2TtW+PACcOwXCzvrNLcyVhG96mICkjzE5+5PX4T6Kw4dREdALi9HrrPaauQJjSSrOxw/gWpiIa/4OvI78H/7JnwJQ4xpKSdhgSloN5XirIVicfc/9O3w6CSYvoHREW4yHivH5eA8+8/fjtewQVR18KbyvM8W3x2L1qP3Tg0uMRtQ7GuH/leTMtXBstoUDo8w4RwtCHtQROMH+U/o07a95yj+83ZGfP27H+g9i6HbjEYZM20v7frkqT1lRFMUOwpEnqi92PXpEyy1bZlzoZSjKJaNNm2sZMiSXOXN21XuMzF0mXruskHu+8qLLSGe7++VO30j2sz/RqehJ5n851uF5dTXHif5+GO45v5ET/xhHuz2L1ViP0+ekxOl4Mh7Hfsbz6Ho8s9airy5ECh1lQf0ojhhBUeQoajza1DmE8+QFp74WlWa8liTj+34CrttzsbgbKL4jlsL74qnucO6A22qSFH5r5eg7Fsq2SnReEHSXjpAHdDiFOx7ZFmc78+P7sayfE0N5oTNtuuczdNo+eo5OQ2/4+7z3K4qi2GuiceJ2KWXP87VTAbKitGDt2l1D//4FzJu3o95jpG838UafQv6xzJvOw+w/BS/zgdUcX36AjlmPMXfuCMcmlVai14zA88j3pF71GUVtxzm46nOwWnDL34ZX+kq8M1bgWpgIQLl/D4qixlEYNc7uYNnlj2x8ZyfgtSQZrcZK2dWtKbg/ntIb2oDu3KktpVttgXLBMtsDgH4jNUKn6fDo7XhKTHWFjk2fteWHt+PIPuiFb6tyBj+4n4F3HcTNu4H5LYqiKJcQewNklWKhKC2YwdDwFAtOfsZ2cBhTVgmGsHrs+AIB+97HO2MV6X3fbdzgGGzHUgf2pjywN0d7vYSxJAWf1K/xTV1Cq9+fpNXvT1IW2IeC6PEURd2M2SXgL91PPtAHwOQFZM0LJnt6f3zn7sX3wz1EjFlNTRtPCu7rTNGkOKw+te+6e/TWiPlMozrDdpx1zicWCr624t7blqfsd5OG0Nt30Z1cLVx1z0EG3nWQhP9rxQ/vxPHV0z1Z/lIXBkxK5top+wmIPPdhKIqiKC2JqgekKC2YwWBt8EN6Jzma22rOKccQ5ObwPFpNCWHb/k1J2GDy4h50uL+jajyjyOnyOPtH/k7CzSlk9noFzVxGxKYpxH8WSvQPw/FJWYqwnH3Y58lg2RLoSt5TvUg6OIGML67D1NqdkKd+IzZyHqEPrMdpT0Gd8zuFC9q8pqdnqpHI/+kxF8DB28xsj60h6y0z5mL77wJqGnS9IZMnf1jDf7eupMfIDNZ/EMsTHW5i1s0DSd4UwN/opqKiKEq9qR1kRWnBjMbGC5AdZS6owCnW8frHAQc+Rl9TTGavVx2PyhuoxjOS7K5Pk931aVwKE/FLXojvoc/wzliJ2cmHwrbjyW8/iQr/7qfWdvqOsvPkBZSMiqZkVDTOu/PwnZ2A96ID+H68l7KrWlHwUBdKr29Ta/qFzt324F7wfRpFq23pF+lPWTjykoWgiTpCHtTh3Nb+6xHRrZB7521k7Es7WDc7lp8/bs+2b9oQdVkeQ6fupcdNGej0KlpWFKVlUjvIitKCOTlZMZka523A0Z1HS1EVujrSC841iX/SR5QF9aUi4LwpZE2q0rczmb1fJ+HWDA5e9wPHWw3FP+lj4r7tSdyybgTsnYWuuugvfarmTvjz1SWAo3OuJil1Etkv9cEpuZiI0atp33Ehfm/vRDt+9o40gNAJfIfr6LTOSPxWA37DNbLnWNgRV8OBsSZKfnPsOGufsArGvryDt1KWcvvbWygvdGL2bVfyRIdRfD8zjsoSQ4Ouk6IoyqVIBciK0oI1Rpk3cfJdxIEAWUqJtbQanaf9D/UBuBTtwaX4APnt7nSoX5PSdJS0upbUQYvZfdsx0vu9h9T0RGyaQpfPQoj86Xbcj2046xPEyUC5fPl95D/R05Z+sXgopmA3Qh7fSEzkPEKm/YIxubiOicG9m0a7+QZ6JBsJe1xHya9W9lxlIrGfibwvLFhN9v9PcXIzM/j+JF5N/JaHl67HP7yML57oxaNRY/jiyZ7kpTmeDqMoinKpUgGyorRgRqOkurphbwMnsxysFvuDMVlhAgmau2Oni3hm/gDA8fAbHerXXCxOPuTFPcD+m7axd9RO8mPuxitjFbGrBtJxSQeCEv+HrqrwrH5VcyeAXqNkTDtSfx7DoS03UzIiCp+P9tCu00LCR67E7ceMOrfpjaGCiJdOHGc9S4/5OCTfaWZH+xqy3jRjLnIgT1kn6T78CE//+APPb15F/NAs1rzTgSdiRzF7/ABS/rh4jwVXFEVpLCpAVpQWzGi0Ul2ta9AYJ3eQrRb7+1grbKXFNDfHAmT37F+p8myHyS3UoX4XQqVfVzL6zSLhtqOkDpyPxcmX1lsepcviUNr8dCduOZv/EvD+Jf2ieyBZ867l4OGJ5P3rMly35RB53XKiuy3GZ+5eRKW51jl1roLge3V0SzQQ+60el/aC9GcsbIuqIWWaiarDjuXBRPYo4P5FG3jj4NcMnbaPxDVhvNDvBl4aeB3bvgnH2sBjyhVFUS5WKkBWlBbM9pBew4Ic3YlSY9KRALnKFuAJZ9tzwpMnL7ern1veNsoDezu2wAvMqneloP0EDozYxN5Ru8iPuQuf9G/psKIvccu64b9/DprpryXWTgbK5mA3cp/rTdKhiWR+PBhp0Ai7bz0xUfMIfG4z+qO1l2YTmsD3eh0dfzDS5Q8DfqM0cj6y2vKUx5go2ehYnrJf6wpufm07b6Uu4ba3tlJ8zIVZN1/Fk3E3sfa9WKrK1PPeiqL8vagAWVFaMCcnS8N3kE90dyjFosYWTWuGP9+Czhck66oKMVYcpcKvi+OLPA8z+RTxNcd4kXTuIYVxpDCaVMaTwYMc40UK+JRytmChtN7zVPp1IaPfe+y+7Shp/T8AoM3G+4j/LIzWm6biVJz0l/YnA2XprKf4zg4c/v0WUtaNoqJfKAHTtxETvYBWE9bgvCO3zjndumi0+8SWp9zqSR0lG63sGWQioY+JvM8dy1N28TBzzUMHeH3/Nzz4xU94BVfy2SO9eSRyLF8+1YOiLNf6XRhFUZSLjPrYrygtmNEoG/yQnu7Eu4i19rv+tZIm2+lwGOwPzp2P24LHKq9Y+yc6j1LWk8NblPAdCFugqJfB6PBGoENSjZkiLOK0OsVS4EQ73LgcN/riTn+ciUM4cFKK1eBOfod/kB97L265mwnc+x4B+98naO87lIQNJjfuIYrDh4Fmuz5VcyfYTugTgooBYWQMCMN4+Di+7+3GZ/4+vD9PorxfCAUPd6VkeFStZeKMoYLwF/SEPaUjb5GVY+9YSJ5gJv1fEHy/juB7dOi97fsdNJ2k16gMeo3K4NCWANa804HvZ8ax5p04LhubypBp+2jT7exca0VRlEuFCpAVpQVrjB1kncEWVFkcCJAx2wJkobf/JpZTaSoA1Z5tHZiodhaOk8H9FInP0csggngaLzkMV7qi4XJWe6usooZ0qkiikt1UsI0SfqBQfArYgmrwiedmAAAgAElEQVRPrsGToXgyBD1+9i1ECMqD+pIa1JcjFW8RkPQxAfs/IHrtSKrdI8jrcD/5sXdhdvY/q55yTVsvst8aQO7zvfGZvw+/9xIIv/n/bKf0PRhP0aSOWD3PzvE+maccdLdG0fe2QDnjXxYyX7EQOFFH6EOO1VOOvjyP6MvzyEt1Z+17HdgwL5rNn7clZkA2Q6fuo8sNR9DUvUpFUS4xKkBWlBbMycna4CoW2ol3EYvZgRQLy4kAWWd/IGYsywCgxr21/YurhZlCkrmKSvYRIv9LEE+ice5ycxrOOBODMzF4MxwAiaRGplDKz5SyjuN8R6FYCFLDjb54cxPe3IQTkfatyzWIY93+xbEuT+KdvoLAvbNo9cdThO74D4VtbyWn4xQq/bsBZx8+UjC1GwUPdsFzRQp+7+4i5PGNBL6wlaJJHSl4MB5TpNdZ853MU/a9Xkf5LtvBIzkfWsh+34LvjRqh03R49BUIOw9jCYgsY/ybfzDy2V388kl71s2O5e3Rgwhud5xrpuyn/52HcHJ1IFFdURTlAlKf6xWlBWuMk/ROBcgmBzpZTwTTmv0BsqEyG4vBHavB3YGJ/kpi5jA3UsUBollNCM+dNziui0DgRFv8uYtIPieeHGLkVoL5N1ZKyBKPsVdEsZ8eZDOdatLsG1jTUxw5ioPD1rNndCL57Sbgk/IlHb/pTszKAfikLPlLPsupYFmvUTIqmtSfxnBo8zhKb4jEb3YC7TsspPW473DddLTOMnFuXTXaza2lnnJ/E/lfOpan7Opl4rpH9zJ9/zLu+3QDLl4mFj58OY+1HcPXz3Wj6OjZO/SKoigXGxUgK0oLZivz1rC3gZMpFo7kIJ/iwFHR+so8TC5B9ZjkTzm8QbnYRATz8eTaBo11JoEONy4jlP/Sgd10lIcJk28g0HNUPMVeEUkSfchlFiby7BqzyrcTGVd8QML4TI70noGxPJO2P44j/otIgne9ir4q39butBJxAFU9gsj8dAhJyRPIf6w7br9kEnXl10T1+wqvLw6CqfadXGOoIOLFE/WU39VjLoKDd5jZEVtD1ltmzMftD5T1Bsnlt6Ty3G+reean/6Nd31xWTe/MP9uN5qO7+nEkwcfusRRFUZpbswXIQggnIcQnQoh0IUSpEGKXEOK6OtpOFEJYhBBlp72ubK61KkpLcfKoaau1/mPoT6S5WmocPGva0XmqC7AY6x9Umcghm5fxkjfhy62NuLLaORFFEP8klq10lCmEylexUE6mmEIioRziRopYgpXaj5Q+ncXJh5z4R0kcl0zytcup8oqh1R/PEL+4NREb7salMPFU29ODZXOYOzkv9yUpZRJH370S3fEaWt/5AzExn+L/5na0oqpa59O5CoL/oaPbHgOxy/Q4RwrSn7KwLbKG1MfMVKXa//9aCGjfL5epX//E9H3fcOU9B/nj6wie7TmcN667hoTvwxr0909RGktxWTGvLHyF4rK6T69s7vmae03Kn5pzB1kPHAEGAl7Av4GvhBBt6mi/WUrpftrr52ZZpaK0IEajLTJpSJqFdvIhPUdSLE5yoBavruY4Fifvekxik8csrFQQxmv1HqO+nIgkmKeII4EOMoFAHqGSnaSKcSQSwhEeooLtyPOd163pOB4xnIM3rGPP6EQK2t2J76HFdPw6nvarBuGdtvwvJ7ac3FGWbgYK/9GZ5MTbSft2GNXtvAl+ZhOx5znOWmgC32E6Oq0zEr/VgO+NGtnvW9jRoYakW0yUbnEssg1sW8odM3/nf6lLGfPSdrL2e/PW8MH8u9sIfpkXTU2VuqmpXDjLNy4nOTOZFRtXXDTzNfealD8127uRlLJcSvkfKWWalNIqpVwFpAI9mmsNiqL8lbOzLcBpSJqFzmD7r9mRHeSTucdWBwJkUykWg6cDK/uTxEoB8/FkKM60r9cYjcWFzrTidTqRTrRcgydDyecTDoieHKAbubyLmfOXSKvy7UT6FXNIGJ9J5mXTcSo5RPTakXT6qj2BiTPRakps7U5Pv9AEZddHkvbDTRz64xaOj47+8zjr0atw3ZBV54cW924a7RcY6J5sJOwxHcXrrSQOMJHQv4b8pRakAw9puvnUMOyJPbx58GvunfcrOoOVef/ox2Ntx/DNC10oyXW2eyxFaQzFZcVsTNiIlJJfE35t8h1be+Zr7jUpf3XBPq4LIYKA9sDeOpp0E0LkCyEOCiGeFULUWnFDCHGvEGKbEGJbfn5Jk61XUf6OnJwaHiBrmkDTObiDfCJAlg4EyJq5Aqu+fgdRlLMVk8jEl9vq1b8pCHR4cg2RLKYzx2gtZyPQkykeJpFQUrmdUjacd1fZ4uxLdpcnSLwlhcNXf4XJNYTwLY/QZXEr2+EjJYdPtT29+kVVlwCyPrnGdpz1U71w3XSMqMHLaHv5l3h9dgBRU3ueslOYIOJlPT1TjETO1GMukBwcb2ZHhxqOvm3GXOJAnrLRSt/bUnjhj5U8ueYHonrls/ylrjzadgxz/9GHrH1nV99QlKawfONyrNL2fmiV1ibfsbVnvuZek/JXFyRAFkIYgM+ABVLKA7U02QB0AgKB0cCtwOO1jSWl/FBK2VNK2dPfv367S4rSUjk52YKgBj+oZwSLA5UORD12kIW5Equ+fhUQSvgepIYn19erf1PT400A9xPLNmLlTvy5mxJWkSwGso84cvgfZgrOPYimpyhqLEnDN7Jv5B8URwwnYN9sOn3ZjrZrRuJx9GeQ8qwH+szBbuT+93KSDk8ka/ZViAozrSetpX37Bfi/vg1dYR15yu6CkAd0dNtjJGaJHqfWgrTHLWyPqiH1CTPVGY7lKXe4MptHvl3PKwnfcMWEQ2z5Iop/dR3JjBuvZt/6YEeycRTFISd3ai0W2/uhxWJp0h1be+Zr7jUpZ2v2AFkIoQELgRrgodraSClTpJSpJ1IxEoEXgDHNuExFaRFO5iA39LAQvVFgrnYggjlx0pt04HhqzVqNVatfSbYyNuBKd/Rc/JUTXOlKa2bRmaNEyHno8SFLPEoiYaQxgTI2n3dXuSKgJ6lXLSLx1nSOdfsX7tkbiVl9FXHLuuF3cD7CYnsw8PRAWboaKLq7E4d230ba8hup7uBL8L83ExM1j5CpP9edp6wT+I3Q0Wm9kc6bDPgM1Tj2roXtMTUk3Wai9A/H8pRDY0uYMGsLMw4vZdR/dpK+y4/Xhw7huZ438uuCaEwN/DCnKGc6faf2pKbcsbVnvuZek3K2Zn2nEbaK858AQcBoKaW9N2UlOHCOq6IodmmMFAsAvZPAXGN/+1MHhFjsD56EpQapGRxcmS3/uIJtuNHb4b4XkoYrfkwkhk3Eyt34MZlilnFQ9OUA3cjnIyyUn3MMk1soR3u+SML4I6Rd8RFCmon8ZRLxn4cTsv2/6Ctzgb8GymiCsuvakPZ/I0nedivHx7bD55O9tjzlUefOU/boqdF+kYEeSUZCp+ooXmMlsZ+JxCtrKPjG4tAHIg//aoY/k8CbyUuZ/OFvSKvgk3v68c92o1nxSjxlBfX7sKQoZzqcdfjUTu1JFouFQ1mHLth8zb0m5WxCNuN9KyHEB0BXYLCUsuwc7a4Ddkgpc4QQscBSYImU8r/nGr9Hj2i5ZcuMRl2zovydrVgRzJgxvdmy5We6dz9e73H+HZVH7NVGbv/IvpzRmtQiDsTMotXHw/G9s8upP587d0SdfbrPdSan41Syek93aG3VpLFXRBIu5+DPvQ71vdhYKKWQxeQzm0qRgCY98WMiATyAMzHnH0BKPI7+SFDiTLyPrMaqGSmMvo2cTtOo9Iv/S1PnyQtOfa3PLsf3g0R85ySiL6iislsA+Q93pWRsO6Sx7rsPllJJzjwLx2ZZqE4D57YQ8qCOwIk6dO6O7XlICXvXhfL9zDj2rA3D6GKm3x2HuXbKPkJi1PMnzaG4rJjZ38zmgZsewNu9/hVlLoT0nHReW/QaT9/+NOFB4Rd6OcoFNNE4cbuUsuf52jVnHeQI4B/YAuTs0+ob3yaECD/x9cm/tVcDCUKIcuA7YBnwSnOtVVFaikbbQTYKLA7sIKM/kWJhduD2u9UCmuOpINUcBMCJWIf7Xmx0eBDAP4hlF+3lb3gxjHzeZ5+IJZlrKGY5knMc5ywEpWGDOTR0FYljD5Afc5ftlL5lXWi/ejBeGavhxG3dv9RTDnYj9z+Xk5Qyiaz3TstTjlmA/xvnqKfsIQh9WE/3fUbaf67HECBIfdTCtqga0p8xU53pWJ5yp2uO8s/V63h553J635zKrwuieSZ+JG+Puor9vwSpPOUmdimXHJuzfA6V1ZXMWT7nQi9FuUQ0Z5m3dCmlkFI6n1Hf+DMpZcaJrzNOtP2nlDJISukmpYySUj7nQDqGoih2+jNAblgOss7gWJk3cSJAxoEAWWClPplW1aQCtlrEfxcCgTt9ieQzOpFBiHyJKg6QIkayl7ZkM/28D/VVe8eQ0X82CbceIbPXqzgfP0C7H4bRaUkHAva9j2auONX2VJ6yi56ie07LU47xIfhfp9VTPlRHnrJe4D9aR+cNRjr/asB7kEbWWxZ2tK/h4AQTZTsdy1MO61jMXR9uYsahpdz4dALJmwOZfs1Q/tvnBjZ/HonZpDLyGtulXHIsPSedo/lHAcjKzyIjJ+MCr0i5FKinHRSlBXN2bpwqFnongfn8B8KdIgy2gFzWceRxraRECsfXaSITpIaBUIf7XgoMBBPCv+hEKpFyKUYiOSqeIpFWpHMXFew6Z3+Lsy/ZXZ8i8ZZUUq5ajMXgScRvDxC/uBVhvz+NoTwLqKWe8nVtSPv+jHrKHRcSPmY1rhvPkafcWyPmCwPdDxgJflBH4UorCb1N7BlcQ+Eqi0Ol/7yCqhj1n128lbKUibM3UVVmYM6EATzefjTfvdmR8iKj/RdSOadLueTYmbvGahdZsYcKkBWlBWu8h/Qc3EE2nEixqKPW7jl6OtgeTBxDTyCChu2SX+wEenwYTXt+ooNMwI87KeILDohuHGQARSxBYq6zv9QMFEbfyv6Rv3Pgxl8pCR1EcMLrdP68DZHrb8M1b/uptqcHy6fqKR86UU9541GiBi0jqu9XeH2eBHV8CHJuI4h8Q0/PVCMR03VUpUoOjDKzs5OJ7DkWLBX2/30yuli48u5kXkn4lkeWryO4XQlfPdOTR6PG8NmjvchNcbf/QipnuZRLjp2+e3yS2kVW7KECZEVpwU4GyFUNPOLXloPsQIBsPLmD7Nitdc53FHMtzORhINDhfpcyFzoTzhw6kUmYfJMaMkkV49hDFNm8hpn8ujsLQVlwf1IGLyVx3CHyOj6Ed8ZK4r7tSczKAXinfVvrcdbmkBP1lFMmkvXeVehKa2g9YQ0xMZ/iP2MHWnHttxj0XoKwR/R0P2Ck/UI9em9ImWJme1QNGc+Zqcl2oBSgBl2uy+LJNWv47+8r6HlTOus/iOXJuJt4d9yVJG8OsHss5U+XcsmxunaL1S6ycj4qQFaUFuzPg0IaWAe5OVIshKjztv25WChCh6/D/f4O9PgQxGN0JJkouRxn2nFUPE0irUnnHipJPGf/Gs9IjvT5H7vHZ3Kk9wyMZRlEr72JTktiCNzzLprJVozorHrK93QiOeF20r8ZRnW0N8FP/0ZM5DyCH92AIaX2aimaQeB/s47OvxnotN6A5xUamdMtbG9bQ/JdJsoTHPswFdG1iHvm/sabyV9zwz/3cOCXYF4eeD0v9L+e35dEYDGrPGV7OVJyrLismFcWvnLe3WV72tk71rnkFefV+ue5xblNMl9jj9WYa/o7a4rrVOvxzbURQrhiq0ARyBmBtZRyWaOtSFGUZnNyB7mmpuEpFhXFjhwUIkA4lmIh0U48qOcYM8U4EeVwv8ZWrS+nyliCRTOhsxhxrfHGYHFulrkFOrwZjjfDqZR7yeMdCviUAvExHnIQAUzFixvqTEOxGj3JiX+UnE4P45P2DUGJ/yN888OEbn+W/Nh7yek4BZN761NBsvPkBaAJSm+IpPSGSJx35eH39k78PkjEb3YCJcOjKJjWlYo+IbYPPqevVQg8+ws8+2tUHpIcm2Umd76VvIVWvAYJQqfp8B6iIYR9Aa5PWAVjXtrJsKcS2biwLWvfjWP2bVfiF1HGtQ/tZ8Dkg7h41J16osALd70AwILvF/Dzzp+5qttV3Dn0zlrbnl7poq429razd6xz+eiJj+xu2xjzNfZYjbmmv7OmuE52BchCiMHA54BfLT+W8DdP7lOUv6nGSrHQGRzcQRYCYdQ5loOs6f5ya99eVkrR4eFwv4Yqcs3ij+jPSQr7kYyA7ZS6nL2T5VLthV9pG4KLYwkt7ETrgm5E5PbCs6rpUkJc6Eg4cwjlFfLlx+QxixQxAqOMIpCH8WMSOjxr73ziOOuiqLG45WwhKPEtghJnEJT4FoVRY8np/CgVAb3+PHQEW7Bc1TWArHnXkvNSX/zeT8Dnoz14fXuYil5B5E/rRslNbU+V/vvLWqMFUTMNtH5OkvOxhezZFvYPN+PSQRD6sI6A2zQ0Z/sCZWd3M4PvT2LQvQfZuaoVa96J4/PHe/Hti10YMDmZax7cj3/EuQ9eacnOrGIxvP/ws2oh29Omscdqzt+vucdq7mtwqWqq62Tvv4pvA6uBVlJK7YyXCo4V5RLVqA/pOXLUNLY8ZEfqINd3B9lKBRpuDverr1LnPOZfOZFnbgtnWZ/HKXTPID5tOCO3vsL4De9zx88fc8uv7zHi95e5LPl2vMvDSAv8nRWXPct71w3jiQlB/PvWKD4dOJmt7RZx3PVYk6xTjx/BPHmi+sWXGAgmU0wjkVYcYRrVpJyzf3nQ5aQM/orEm1PI6TQV74zVxH17GTErrsA79ZtTH2ZOT78wh7mT81JfklImcfTtgeiKqgi/7Xvax36K3/92oB2v/VOWwVfQ6gk93Q8aiZ6rR3OCw/eb2da2hiMvmqnJdSBPWSfpMeIIT//4A89tWkWX6zJZN6sDT8SO4v3bB5Dyh7/dY7Uk9lSxsLfSRWOO1Vgac77GGutSrhzSnJrqOtmbYtEGGC6lPHq+hhez0lInCgp8MZlUTK84RghwcakiJCQf7W+Uuf9nmbdGyEF24CE9oB47yHqE1fFb4VYq0XBxuF99HAr6jfeHjKDKWMLVidMYsO9+Akui7epbZSjliN8u0gJ/51DwRna3Wc6m2HkAhBXE0znjBuLThtMm9zK0Rnx8xFb9Yhw+jKNcbiOPt8njPfJ4By9uJJBHcGcgoo4KIjUeEWRePoOj3Z/HP2kuQXveJnrdKKo8osjtNJX8mMlYDe5/Sb+QbgYK74+n8N5OeKxOw3/mTkKe/I3Al36naHJHCh7sgqnN2bvYmlEQeLtt57jkF8nRmRaOvGgh83ULAbdphD6swzXO/msT1bOA+xb+ythXtrN2Vhy/fNKOrV9F0r5fDkOm7qPbjUfQdOr0kbqqWJy+U2dPm8Yeqzl/v+Yeq7mvwaWqKa+TvQHyb0AMcLhBs11ApaVO5OcHERYWirOz0e78NUUBsFolR4/mUFhYjb9/6YVeTqMxGCRCyAbvIBucHTxJD8cDZCl0IB1PsZBUI3ByuJ+jkoN/5d3rh+JT3orHVmwgtDjOof7OJg/aZV9Bu+wruCbhMaxYOeK/kwNh69jb+nvWdHmd77u9imd5MF3SR9AjZSztjg5EJ+1+lOS83OiJGwsJZTr5zCafOSSLFbjILgTyCD7cglbHtbQaPcntPI3cjg/hk/YtQYlvEb55KqHbn6s1TxlswXLp8ChKh0fhvD0H/5m78Ju1G79Zuym5qS3507pReVnwWXMJIfC6UuB1pUZlkpWj71jIW2gld64V76EaoVN1eA0Sdr/P+7Wu4Jbp2xjx7138Or8dP7wTx7vjriKwbQnXTtlP/zsP4ezecvOUz1XF4mS+pz1tGnusxtKY8zXWWM19DS5VTXmd6vxXUQjR/eQL+AB4UwhxtxCi9+k/O/Hzi15BgS9hYaG4uDip4FhxmKYJAgP9KSlp/lzWpiSELc2iwWXe6pNi4aRHVjsQINdjB1kikaIGQdMeGFHqnMdHg8fVOziujYZGRH4Phux+kkdX/cQbn+Yy6cdFRGf35/d2i5g5bDBP3RHK4v73kxyyAWs90k/qYiSUUF6iExmEyw+RmEkXE9lDBMd4ARNnVwD4c+F6iqLGcGDEJvYP30xJqyEEJc4g/otIItePxzVv26mmp6dfVPUIInPhEA4enED+tG64r82gbf8lRA5ciuc3h8BS++/nEqPR9j0DPVKMtH5eR/lOK/uuM7G7p4ncTy1YHfh76eJh5top+3l9/zIe/PxnPPyrWDStN49GjWHJv7pTlOVq91h/J/ZUsbC30kVjjuWIc1U5aMwqHY219qa4BhejhlafaMrrJGQdZZOEEFZsD+CdL5qUF0seco8e0XLLlhm1/iw5uRUxMVEqOFbqTUpJUlIK7dplXuilNKqAgOu5444M3nprT73H+OapUn79oIK3ioPs7nOg43u4dA0m4rPRp/5s7twRdbaPXxTC8fBhpA+w/6l0iZmdwkCIfIEQnrW7n6NO5gs/vewPWhV2abJ5TqrRV7C39fdsa/slieGrqDFU4FPaml6Hb6X3wTsIK+rUqPNJJKWsI5eZlIjvENIJX8YTwDRciT9vf2NpGoF73yXgwEfoTKWUBvUnp/OjFEcMtz18eYLz5AWnvtZKa/CZvw+/WbsxppZQE+VJ/kNdKZ7QAatH3R94rNWSvC+sHP2fhcp9EkMwhNyvI+heHQY/x9//D2315/u3OrL92wg0neSycakMnbqPiG6FDo+lXDj2VOBoznEUmwtxPScaJ26XUvY8X7tzbRtFAlEn/nuu14Wvn2QnFRwrDfF3/fvj7Gyhqqphn3EdrWIBoDmaYqEZENLRHWTb+E15il62VxKbYucxKHFaswTHAEazK91SR3HPui9549NcJv/4GWGFnVkXP4MXx3XmlVE9Wd/pHcqcz3EgiAMEAk+uIZrVxMn9+DGJIr7kgOhCMtdwnO+Q59jBrvFoQ+blM2z1lC9/C2P5EaLXjaLTkhgC9s6qtZ6y1cNIwZSuHNx3BxlfXIcpyI3QRzcQEzWPoKd+Q59ZVutcmpMgaIKOrjsNxH1nwC1ekPG8he1RNRyeYqLyoGM77dG983noy1+Yvn8ZVz9wgJ0rwnm+941Mv/Zadn0XhrXxNu6VJnJmlYP67lY21jiKzcV+PesMkKWU6SdfQASQdfqfnfjzrBM/UxTlEuXkZG14DrKTrWiB1eLYaXoOB8hWk4MrOxm9NN2Tlb90nI3eYuSahMeabI5zcTK7cdmh8Tz0/WqmLzzG2N9mIrHyVb+pPHl7KB8OHkti6++wiMbJoXUmlnDepxNHCJWvUsU+Dosb2EcceXyAhbpLpVmNnuR0foTEmw9x+OqvMDsHELFpCvGLWxP2+1MYymx3Z04PlNFplIyKJvWXMRzeOJayweH4z9xJTPsFtJqwBucdtad7CCHwHqwRt8pIlx0G/G/RyJ1nZWdnE/tvMnF8g5W67qDWJjCqjPFv/sGMlCWMe3UbOYc8mTlyMM90HslPH7WnpvKiuJGq1EJVlbg4XezX095/NX6CWo+i8jrxM0VRLlFGYyPkIJ+oRWuqsr+PcNI7FiDrjPUIkE/NVs9+52YRZv6IXkx82gg8K+1PL2kqHlUBXL1nKv9atoNnlyQwcO+DJIX+xHvX38C/xrdhZc/nyXdPa5S59PgSzFN0Io028jN0eHBE3M8ewsniGWrIqrvziXrKB0ZsZv/wTZSEDSY44Q06fxFJ5E+345q/AzgjUAYqLwvmyOfXcfDAnRQ8FI/HqhSiL/+SyMHL8FiZAtbaA163ThrRcwz0OGyk1TM6Srda2TvYRMLlJvIWW7Ca7A+U3bxNXP/YXl5P+pp/LNiAs4eJBQ/24bG2Y/j6+a4cz2mew18U+9RV5cDR3crGGkexuRSup73/Kgps+chn8oNzbBcozWLQoGFMmfJ4k88TFRXPjBnvNnicn3/eiE7nQ35+gd195s9fjKdnqwbPrZzN2dnSKGXewLEH9YSTzsGH9Oqzg9y0UoI2U+aST4+UsRd6KWcJK+zMuM3/Y/qio9y7ZilhhZ35rvuLPDs+inevu45dbb7FojX8egoM+DKeGH6nvfwVdwaSw3T20IZUbqeCHefsXx7Uh5TBS0gcd4i8jg/hnb6cuG960H7VVXilrwRpPRUonwyWTW08yX79CpJSJnFsej8MqceJGL2adp0W4ftBAqK89t/LGCQIf15Pj8NGot7TY62A5IlmdsTUkPWmGXOR/X9/9QZJn1tTeX7zap5c+z3RfXJZ9Vo8j7Udwyf39OVIoirFdTE4V5WDCzGOYnMpXM9zBshCiBVCiBXYguNFJ78/8VoNrAU2NcdCW6pJkx7gxhtvPmebpUsX8sorz9Vr/KlTnyQmpketPysqKsbNLYQPP5wPwNat67n//rvqNc/p+va9jKysA/j51XZTonY333wThw7tbPDcytkaI8VCf6Lyl2MBsh5rtf23/aVmQDhaS+7P3vXsd277W61FWDXiMq9tkvEbg95qpHvqaKb83//x0uJUrt/xLFm+iXww5CaeHh/Oip7PUuie0eB5BAJ3+tOWZXQkmQAe5DjLOSB6cJCBFLP83HnKnpEc6fM/EsZncqT3mziVptBuzXA6fRVLwL7ZaCbbXsxf8pS9nCh4pDsHkyaQsWgIFm8joQ//Qkzb+QQ++//snXdYU9cbxz83CQQEWbJEBFEQFUQR67Zura1aV617V6u1Wu20tfVXtdo6q1Zra11177pHrXvWOpElQ8EJoiCyQ3J+fwRQlJFAUGvzeZ77GHLPPefkmvHe937P9z2F4nb+OmW5uYTze3JqXzKh2h8KzL0kor9U80/lTKLGZpEeqcf7WILqzWIZs/kQ065s5fVB4ZzZ4MHXAW8z863WBO53QQ8lhxEDY3SVeDn5N5aI06oAACAASURBVJzPAl0sACRJWpb9cACwAUh7YncmcB1YLIQwzEqQElKUi0W1alUMMs6dR3fptWUI67otxdmydG+rDho0kvj4++zYsf6ZfZmZmZialsy+6tKlQOrUeZ2DB3fSrFnjPPsWLPiV8eMncetWCGXLFm1vZoj5vOyEhka+ci4WLVo0wcREw/79xb/WPf17GquGJvG/MHvsPXTLRl/vup7MmIdU/WdY7nOFuVhU29YQtUlZwt/cr/O8NKRzUTLHRUzFmfE6H6crc99syyPzOCZsvmjwvksTtZRFkNsejlX/hStuu0FI1Ix5i2bBI6l+o63BCpGoeUg8S7jHXDKlGJSiCg58RDkGIsey8IM1Wdhe24xz4Cws7p0lS2nLveojiPMZhapM+TxNc90vhKDMyTvYz7lA2R1RCIWMh+9W5f6Y2qTXcih0uJSLGm7PVRO/QYNQg10nGS4fySnbUHc/5RyS7ys5+GtVDi6qRuKdMrj6JNB2TDANekZhamZc1acricmJLNy6kJFdRhZY9EGXNobuy1Bzf9V5Wc+BIVwsEEIMEkIMAr4FhuT8nb0NF0JMe1mC4+fJlGMzOHHjNFOOzniu4+Zkk6dP/xE3Nx/c3HyAZyUWW7bsoHbtxlhYlMfe3oMWLd4iNjb/hSy1atWkbl1/li1b9cy+pUtX8c47nXOD46clFnK5LQsXLqZbt36ULVuBr76aDMCuXfuoXv01ypRxpnnzN1m3bjNyuS3Xr2uzVE9LLHLkE3/9dQQ/v4aULVuBVq06cu1adO5Y+Uksdu/eT8OGrbGwKI+DQ2U6depJerpWBLtq1Xrq12+JtXVFnJ296NFjILdu/asLQZYaWolFCTPI2ddF+kss9MkgF0eDnPO6SieFd9P+Im7x+d+BeZmRCwV+0R35YO9Opqy5RruLX3DN8Qzz32zPNz292F9rBinKktuYybHGiXH4EImHWI8CB25KH3KFitziczIp5GJTpiChyruEvH2G0I7HeFS+Oc4Xp1FzrTuVDg/A/P6l3Ka5WWVJIrWxCzGb3iI8qB8J7/litTUSz9fWUemNrVjuvV6wTrm2DK9lJgSEm1LhYzlJRzRcaa4isKmK+I1qRJbu7yHLchl0Gh/IzPDNDP3tOEiCpcMa84lnd7Z950fSvdIvXPMqsO34NsJvhhd6212XNobuSxcM2de/lX/7OdDpV1EI8a0Qwqg1Rps9Xn5pDRqhYfml1dxNjn2u4x89epLLl4PYvXsjf/75xzP7796NpXfvIfTv34ugoDMcPryLPn0Kl2gMGtSXzZu3k5SUlPvc+fOXuHgxkMGD+xZ67KRJ02nfvg2XLp1g5MihxMTcoHv3/rz5ZlsuXDjGqFHD+eKLiUW+royMDH74YQ6//fYTJ07sIzHxISNGjCuw/d69B+jcuTetWzfn7NlD/PXXdpo1a4wm23MpM1PFxIlfcOHCMbZvX8f9+/fp02dokfP4L6ItFPIiNMj6L9KTqfXzkpOyv+Jy7N4MSbLyPo/M7+HywMfgfT9PyiW70/nsd0xbfYOhB9Zhm+LKlgaf8UXfCixvPpBo+3+K7qQIcspZe3OKquIkZWlDLDO5ggfX6E0KhYwhSSQ7NyGyzRauvBvOvervY3ttMz5balN1V2usY3ZBtpbxSflFpqcNd35sRljUQO5+1whlWAKVOu3As/ZqbJdcQUrL/+LM1EXC/TsFAVGmeMxVkPUArvbJ4nz1TG7PzSIrSQ+dsqmGJv0jmXxuB5/t20elOvfZ+q0/H1fpzvKRDbgd+mw5bSNadLEA09UmzJB9GWrurzqvwjkorJLeNUmSonTZnueEXzRTjs3IFZarhea5Z5HNzJQsWfITvr41qFnz2R/m27fvolKp6NatE5UqueHrW4OhQ/vj5ORYYJ+9e3cHYN26LbnPLV26kmrVqtK4cYNC59OjRxeGDu1P5cqV8PBwZ9GipVSuXIlZs77D29uL7t3fZvjwQUW+rqysLObPn0G9egH4+fkybtwojhw5XqAN03ffzaBbt05MnjyBGjWq4efny8cff0iZMtpKV4MH9+XNN9tSuXIl6tULYMGCWRw7doqbNwtZWf8fxdTUEBrk7ABZD4mwvjZvGpkpkkZfDbI28C+NAPmetVYr55jkZfC+XwQKjSl1I9/l4x1H+HrjZRqGDeKCx2amdXuNHzo34LTX76hkeppd54MlDanMBnyIxJHRPGQXYdJrXOV1Etla6P9VhlUVbjSax+XeN7hZ7wfMHobita8DPpt8sA/5FSlLqwJ8clGfxtaM+E8DuBo2gBvL2iDMFFQYcQhvz+U4fnsaeVxqvmPJLSTKj5DjH2hCtU0KlBUlrn+q9VO+/nkWGTH66ZRrtLjLuO1/MfXSHzTqE8XxlZ586deFOZ1bEnLY2ahTfgpdLMB0tQkzZF+GmvurzqtwDgr7VfwJWJC9rUDrWBEJrMreIrOfW166U3x5yMkeZ2YvFMpUZz73LLKvb3WUyoJvz9Wq5UurVs3x82tM9+79+fnnJdy7p1XBxMTcwMrKNXebNk2r17aysqJ797dZvnw1AOnp6axdu6nI7DFAQIB/nr9DQ8OpWzfvc/XqFSn1QalU4u39ONBwcSlPZmYmCQn5X3VeuBBIy5bNCuzv/PlLdO7cGw+PmlhbV6RevZYAxMS8WvphQ2AQiUUxFunJlHI0erlYmCLpnUGWQEhQCgHyfUutBKjco0oG7/tFU+FBTXofX8j3q2/S48RcUk0TWd5yAF/20S7qSyhT8gtNJZVwZRY1uUEFMZtMYoiSuhKMN3HMR03+C+wA1Epb7tb6jMCe14hqsQqNogyVjg/Hb60bLucmokh9/J2cEygLUzkP+1Qj8sy7RB3oSmo9Zxy/O4t3leW4DP8LZXD+khJJLmHXSY7vQVP8Tplg217G7XlqznlnEtZHxaN/9NMUu1R/yKCfTzE7chNdvrlA1Fl7fmjbjon1OnBiVWWyMkvPs/vfgi4WYLrahBmyL0PN/VXnVTkHhRUKmZWzoa2Y94MQoo0Q4pvsrQ3wPVD1eU32RfNk9jiH551FzsmQFoRcLmffvi3s3bsZPz8fli1bhbd3AJcuBeLiUp7z54/mbsOHD849bvDgvpw58w/BwaFs2bKDlJRU+vfvVeR8LCwKn4+uKBSKPH/nLIrRFKNMVUpKCu3bd6NMGXNWrFjEmTN/sXv3RkArvTCSF0NKLFTpekos0vXQIMuVyPTOIGtv7wsMUyTjSRIttEGiTfKraz9onmlNyyuj+d+GEEbv3E+le/XYU+c7vurjzuLW7xLhfBxRQn23HCucGIsPEXiIDShw5KY0+gmd8o0CjxUyEx549iGk8z+EdjhMimNDXM5Pwm+tG+5HhmD24HH59Fw/ZUki9fUKxGztwNXAviQMrIHNuqt41V6Ne8dtWByIoaB0rmWAjKorTQgIM8VljJzEfRoCG6kIbJHJ/T/UCD0K5Vg5pvP2hMvMitzEoF9OkJUpZ/HgpnxStRs7f/Al+cGrveC5MHSxANPVJsyQfRlq7q86r8o50PVStStaF4un2Qh00qUDSZKUkiQtkSQpWpKkR5IkXZQkqX0h7cdKknRXkqQkSZKWSpL0wlc1nLp5Njd7nEOmOpOTN/9+QTPKH0mSaNiwHt988zlnzhzExaU8GzZsRaFQ4OlZOXezs7PNPaZp00Z4e3uxdOkqli1bRceO7XFwsNd77GrVvDh3Lu+K/rNnz5X4NT2Nv39NDh48ku++0NBw4uPv89133/D6642pVq0qcXH/ubWkOmNmZoBKemY5GmTdj5FM9VukpylGBllL6QTIj8xjUahNKZP58qzOLi0kJGrcasMHe3cweW0kLQPHEOy6j5lvN2Vq1wBOei9DJdejSky+Yyiw5R28OYm3OEVZWuunUy7fjIh22wl8J4x478HYRa7Fd3NNvHa3w+rmfhDiGT/lTG9b7sxvTljkQGK/bYDZpXg83tyGZ8BabFYEIxVwh0PpJlHpe61OudJMOZm3BGE9sjjvk8mdhWrUKboHyqZmGpoNimDKhW2M236ACjUS2fR1AOMqd2flmPrERhTtIFQUicmJTF05tdAM3vNsUxS6WIDpahNmyL4MNfeXmef1/2fI8UoLRdFNAG0xkObA06+uOZC/gCv/sW4AzYAY4E1ggyRJNYUQ159sKElSO+ALoCVwG9iK1knjCx3HKhXODzv6IofXidOnz/LXX0do27YlTk4OXLgQyI0bt6he3bvIYwcN6sP338/h4cOkfG3ldGH48EHMmbOQTz/9mqFD+xMUFJrro6ynU1KhjB//MW+/3QtPzyn06tUdIQR//nmIYcMG4ubmilKpZMGCxYwcOZSQkDAmTpxquMFfMV6Yi4WZAqHSIDQCSVb0m0PIlcXQIGsDL0ohQE42i8civZxWxvEfwv6RB91Pz6LjP5M447WKQ77z+L35YLbU/4zXg9+nafD72KZWKNEYFjSgMhvJ4Dr3mE88i0mQ1mIpXseRsVjTEYn873pk2FQlpsnP3Ko7BYeQX3AMmk/VPe1ItfUltuZYHlTpjVCY5anQZzZ4BffGv0b8uDpYrwvDfu5FXN/7C6cJp3gwwo8Hw3xR25s/M5bCSsJltILyI+Xc/0NrE3ftoyxufAtOQ+Q4fyBHWUG394dMBn5v3MLvjVvcuGzLvnk1OPybFwcXeePf8QbtPgqiauO4Yn2PPukm0P+N/i+8TVFMGjLJIG0M3ZehxnuZeV7/f4Ycr7TQ9VdxDrBAkqRFkiQNzN4WAfOz9xWJECJFCPE/IcR1IYRGCLETuAbk55E0AFgihAgSQiQAk4GBOs71P421tRUnTpymU6eeeHvX5dNPJzBhwif07Vu4kwVA//69SElJxdXVhXbtWhVrfHd3NzZuXMGOHXvw92/K3LkL+frrzwEwMzNcCdY332zL5s0r2bv3AAEBzWjRogOHDh1DJpPh4GDPsmUL2bZtF76+DZg8eTozZ04x2NivGtpS0yWUWORkkPWQWMiU2QvodFyoJ+RKvV0sQFvpTWB4aU2qMoEyGbZFN3xFUWZZ8HrIcL7ZeIWPdvxF5dhGWvlF70r81qoX1xxKfmftsU75JhXELDKJJkrqQjDe3GNB4Tpls3Lc9f+SwF7XudZsOUgyPI4OwW+dO+XPT0aR/viuUk6wLJRyEgfUIOJcL67tfpv0WvY4/e803lWWU37UIUzDEvIdS1JI2HeX43fMFN8jJli3kHFrtprzVTMJH6gi+YJ+UrGKfgkM/e0EsyI20+HzQK6ecGRay/ZMbvImp9dXIkule5RsKAeH5+0EYeT587z//17290uhhULyNJSkHsAYoHr2UyHAXCFEftILXfpzAqKB2kKI0Kf2XQKmCiHWZ/9tD9wD7IUQ959qOwwYBuDm5hAQEbE43/EMWSjEiH7Mm7eIiROn8uBBtN6G+y8br2KhkEmTvJkypRrp6duQFTOR/CBazTde8fT51YqGA5/NtOXHvR9Pc+ezP/G59ylya+3FU2GFQlxPjcMh9FcuDCo4KMqPyzhjw9u48YtexxXFj2+1IVORwmfbjMVEc7hnFcmRGgs5Xu030pVJeMTWp2XgGOpc645cY1Li/gVZJLKFWGaRKv2NXNhgz3Ac+BBTishaC0HZ23/hHDgb6xt70MjNuO/Vn9iaY0m3qZanaW7hEUAZdJ9y8y5isyYMWYaapLc8uD+mNinNKhR6Wyz9muDOfDWxy9VoksGquYTLGDm27WU63TF5koxUOcd/92T/vOrERlhTzi2Z1iNDaTbkKmWsC7/4W7F3BUcvHUWtViOXy2lWq9kzmbrn2cbIy8vz/v97Ue8XgxQKeRIhxAYhRGMhhF321rgEwbEJsBpY8XRwnI0l8PCJv3MePyPGEkL8KoSoK4Soa29v9JR8GVi4cDF//32Oa9eiWbt2E1OmzGDAgN7/+uD4VUWpzPGOLr7MonilprMzyDo6WRRfYlE6GeQMk0eYqUquD32VcEiqQvfTs/h+9U3ePT6fFOUDlrTuzZe9K7HHfyrJyvtFd1IIj/2UT2f7KbcmlhlcoRLX6EsqhZSjlyQeVWhN+Bu7udI9mPte/SgXvgLfjdXx3NuBsrcO5i7Oe1KnnOFTjtu/tCIsYiBxX71GmTN38Gi7lSoN1mO9JgxU+b9/zTwkPGYrqBtlivs0OekRgtAuWVz0U3F3sRp1qu6fFWUZNa3eD2PalT8Ys+Uv7Csls/6Luoyr3J21n9bl3nWLfI8zlIPD83aCMPL8ed7/f/+G98tz95ORJEkGrERbqnpUAc2SgSej3ZzHj0pxakYMRETENbp164ePT30mTpzK8OGDmD79363LepXJCZBLokPOlVjoWSgEQKPjQj2ti4UqtyiEzuNgggb9A+uiyFSkYpJlGBeXVw0zVVlaBI3if+tDGblnBy4PfNhW7yvG93Vl5evvcdsmuET9S0jZfsob8SEcBz7gIdsIlepwlRYksgNBwe+TdNvqRDf9lcu9YrhV539YxJ/Fe3cr7MOW5G33RKCsdipD3MQGhEUO4tbPLZBSs6g4cD/eVVdgP+McsoT8FykqbCQqfKygTpgpXisUyCwg6oMszlXJJOZ/WWTe1UOWJAP/DjcZf2Af/zuzg9pv3eTAgup8Vq0rC3o1I/LvvAurDeXg8LydIIw8f573/9+/4f1S4CI9SZKSgMpCiHhJkh5RSK1WIYROqVtJm0JcAjgBbwohCkrrBAG1eOycUQuIfVpeYeTlZPbsqcyebVwU92/BIAFyrs2b7sfITPXLIGvk2jS1pM5EKHTXs0uYlkoGWSVPx0RtOF39q4gMGX4xHfCL6cAt2yscqjmPM14rOVH9N2rcaEuLwDH43HgDWQlyNUoqU5EfceFb4sVi4phHlNQJpaiKIx9RjgHIyP9CJsvckTsBE7lb63PKRawiwaN7vu2eXtCXMMSXhEE+WO6Lxv7HCzh/dRKHqWdJ7O9F0jsVyXI2J8OzYt5zYSLh0EuOfU8Zj04Ibs1Wc3Oamlsz1Tj0klF+jBwLX93PQyX/B7z/+zF6TD3HgYXVOLTYm7ObK+HZII52HwUR8PYNgzk4PG8nCCPPn+f9//dveL8UqEGWJGkAsE4IkSFJ0kAKD5BXFLTvqT4XAbWB1kKIAoWEkiS9gbYASY6LxRbgbyFEoS4WAQGe4vTpWfnuM2qQjRiCV1GDvHSpG++/709ExH7c3NKK1YdGIxhtFkf7CRa89Y2lTsckbgwips8Wqp4fjpmvY/ZcCtYgO12eRcUzn3BhQCJqU2ud5xaMH0qqUIWtOh+jC1/2rkTV280YeFinrz8j2SSbxXO0+i8c8VnIQ4vbOCdUo8WV0TS42h9lVv5SAX0QqEhgE3HMIVU6i1yUw57hODIKE8ob4BXk1SgDmF26h/3ME1ifPwSyLIRVFulV3bk+/yM0lgXfZUgL13Bnvpq43zVoUsG6tYTLRwps2kh6S9LSHim0OuX5NbgXVRYHj0e0/TCYpgMjMLMs+i5NYnIiC7cuZGSXkdhY5m9dGB0bzfervmd83/G4ObnpNb/ijGfEeJ5KgxJrkIUQK4QQGdmPl2f/ne+my4QkSXIHhqMNkO9KkpScvfWRJMkt+7Fb9nh7genAIbSWcNHARF3GMWLEiH6YmpY8gyyTScgUxZRY6Ohi8TiDrJ+ThQxTRClILNQylUEWnv3XsEy3580LXzF1zXUG/7Ua0ywL1jYdyfg+Fdla7wseWBRcGEQXJEywoxfenKGqOIYlTYllGldw5zoDSeVSiV/DM37KXmVRyi7wqL0nD1q/iSYigDKnY6nS9hesNlyFrPzlHuZeMirPMyEg0hS3yXJSgwQhHVRc9FdpF/fp8XkyL5tFmw9C+SFoK6PWH8LaOY3V4+oz1uMd1n8RwIObhcuBnrTbKohftv1CWkYav2wr+YJXXcYzYjxPLxKdfhElSfpSkqSGkiTp6pv8DEKIaCGEJIQwE0JYPrGtFkLEZD+OeaL9bCGEkxDCSggxKCdYN2LEiGExMyt5gAzaYiFZesShMjPt14muxUKEXCtn0L/cdOkEyBopC5ko9lfifx65xoR6Eb0Zv+Usn/xxHO/bLdlfawYTelVmScs+JbaJ0+qUm1CFrfgQjj3DSWQjoVJtwmnDQ/YUqlPWlfQl/bHbeAB5cioxMz/kzpy3CIsaRFotRxTp93Dru4+q1X6n3I8XkCXl/z40KSfh+rmCgKumeP6mQFJA5LAsznlmcmNKFqp4PXTKckHdLjFMOLKHCcd2UbPNLfb+WINPq3ZjUf+mXD9v98wxuthtRcdGczv+NgC34m8RExvzTBtdedntvV4WjOfpxaLrL2J7tNncBEmS9mcHzI1KEjAbMWLk5cAQLhYAJmb6+SBLuQGyfhlkfb2QSy9AViMTJfOPNqINZD1jGzP8z01MXhtJi6APCXTbyQ9d6zP97cZc8NiCWipZoRclVajIfHy5iYuYRjrBREpvEoIv8SxGQ/GkRQCKtDjsVp7ipvfc3IyyLCuDtFrlifu4KdGb3kLlXpbynx3H22Mpzp8dwyQ6Kd++ZEoJx/5yap01ocYeEyzqyLgxSc25yplEjlSRGqpfQO9ZP56Ra44yPWQrrT8I4eIuV/7XoCPTWrfjwo6KaLK7e3LBVEELpZ7OGpcki6zLeEaM5+lFo9MvohCiKWALdAHOoA2Y/0IbMO8rvekZMWKktDEz0waoJa6mp5SKZfOmSdcxgywrnsRCwhQNhr8BJSQNknjuRkCvNPbJlXjn1Gy+X32THifmklTmDr+07cbXvTw5UHMOaSb5B5a6osAWZ77Ah2u4i5VImBEjDeMKbtxmIiri9J/z1WWoFZY88OwFaOUXsnnVkJ8vQ5a9DY86Vebaga5EnOrBozc9KDf/ElWr/Y5r792Yn72bb5+SJGHTSkaNbSbUvmSCQx8Z91ZpuOinIqSzioeHNOhawwDAwSOZXjP+YXbUJt794Szx1y2Z260l4307s2NhOY5fKtxu68nscQ7FzSL/G+y9XgaM5+nFo48PcpoQ4gDwE7AQ2AwogaalNDcjRow8B3IyyCWupqeUyNIjDn3sYqG7zRuATKNvgKwslQwygCSM3t6lgZmqLC2vjGbSunCG79uCXbIbmxqNY3xfVzY0HEu85fUS9S/DlHL0pRrn8BKHsKAhd6VJXMGNaIaSRpDuc00M4aF7x9y/TR9FY31zL0KmIPbGAu2Tag3pAU7cWtyC26v9SW//COugvVTpNg+P5puw2hoB6vyzw2Wqy6jys1anXPFrOY/Oaghqp+JyfRVxq9RoMnUPlMtYq2g/NpjpoVsYseoIFraZbP5zN6qMvO/jp7OVBWWLi5NF/jfYe70MGM/Ti0dXDXIPSZIWSpIUAkQB7wHhQBu0mWUjL5CWLTvw4YefvuhpFIuIiCjkclsuXgw0SH9ZWVnI5bb88ccug/T3X8AQNm+gLRZSnEV6+tu8vRyL9IyUPjIhx/96Fz7ZfpQvtvxNzeiOHPadz9e9qvBLm25EOpWsiqGERFmaU4Xt1BChlGMwD1hDiORLBG+QxH5EwQZOACQ7N0WZFKX9Q6PG/upSzBOCiKsxCmRyMhb3Iv33wWT8+i7O89dhc+AoD7vW4saMvqhqZGL+6ARufbdR1WcldgsuIUsuQKfsIFHxawV1I01ZY9WXORff47PBgxlsOZCBpgMYaDqA0RV75HtsdGw0I2aNyM34yhWC+j2u8/Xx3Tg13weKvGM+bbd1L/Fevv3GJeqfcTe0vdfTr60gEpMTmbpyaokzsIbqp6i+SsMGzZBz/y+gq4Z4HdpSzzOBBUKI1NKbkpEnGTRoJPHx99mxY32BbTZtWomJSfHk4GPGfM7evQcICzv3zL6EhERcXaszZ840hg0bWKz+i8LDw51bt0Kxty9XKv0bKRpDuFiANoOs0keDrHw2gzx48LYCrd5EsTXISkQpSCwAhKT76zVSMirde40hB1fT9cwPHPZZwLHqv3Ch8hYqxdajVeBHJS5nbYY3bizEhUncE4u4x09ESO0wE744MhY7+iBD+cxxyY4Ncb48g+pbA1Cb2iDPTOJurc9JqtgOACFp3+dOV+aijEknoWJ/7j0agUnf7SS1rYfV/tPIb5lguywKl7FHcfr2DA+G+HD/g1pkuT5rmSgzk0hOyt+RIinWnLQIgbln3ozwk+4T3w37Lvd5SYIfxnwDQFxkWfbNq8GxFVXITDXBsuVtLlcIxrftLRZ/thjQlgY+fOEwLfxbFLsk8KQhhi0aVdBre5on3SBKUs7YUP0U1Zehz1NR4xl5Fl1/EYcB+4EPgduSJO2QJOljSZLqSP+h+sEuLlbI5TbPbC4uL6bEdWam9qrfzs6WsmWLV/J28OC+REREceTIiWf2rVmzAblcTq9e3YrVt0ajeeYK+GnkcjnOzk4oFC/Pes+c8/pfwZASC5UecejjSnr6ZpD1qEZC6WmQJSFDSCV3QTCiH7YprnT5exrTVt+g5/GfSFMmsqR1byb0rML+WjNINS1ZdkyBPeWZgC/RuItlSMiIkYZwBXfuMJks4vO0T7fz4UqPMO5VG06cz2jC2+0goXJ2wRGNGmRylEmROAQvoEz8eZTJ1/HZXJNyw4NJX9Kf+KjpJAwKIOroO1zb3Z70hibYzzmPd9UVuA7Yj9kF/bK0F3wyCe2uIumEVqesq/uEY5VH9Jt7hjnXNvHOd+e4HWrD7E6tmVD7bY4s9SLu3qOXzlFB19dmKDcIQ7pKPG+HCqMjhv7oukjvNyFEPyGEGxAA/AG8BpyCp74tXmFiY/M/XQU9b2gGDRpJx47vMn36j7i5+eDm5gM8K7HYsmUHtWs3xsKiPPb2HrRo8Raxsfl/ydaqVZO6df1ZtmzVM/uWLl3FO+90zg2+ExMf8t57o3F29sLGxo2WLTtw/vxjT9HffvsdOzt3duzYQ82aDTEzcyQ8PJJLlwJp3boTNjZuWFtXpE6dprkBl57XXAAAIABJREFUeX4Si+DgUDp16omNjRtWVq40adKW4OBQQBt0T5r0A25uPpibO1G7dmN27NhT6HnLGd/CojwODpUZMmQUSUmPF/v06zeMLl36MG3aLCpWrIGHh1+h/b1qGGqRnomZfhILvW3eZMXLIMtKKYMsE3I0km7BvRHDo8yyoHnQB0xcH8LIvdtxSKrClgafMb5PRdY3Gs09q8gS9S9DSTkGUo2LeIo/KYM/d6RvCMSNGEaQTmie9vHVh5FY6W2yyjjjdHkmjlfmg0x70WkXuY7MspW41mw50U1/5eob+7CMO41Jyk00pmVJXzoAp4UbcVqzGpnNdTSNg3n0jgVld0ThWX89ldpsoezOa6Ap+vPl+rmcpOMarrRQEdhYxcLfF+XZX5Ru2MI2k7c+vcLMq5sZtuwYCqWaZe834qvRl8nKLkj5smhhdXXWMJQbhCFdJZ63Q4XREUN/dP5FlCRJJklSfaA70APoAEjA1VKam5F8OHr0JJcvB7F790b+/POPZ/bfvRtL795D6N+/F0FBZzh8eBd9+rxbaJ+DBvVl8+bteYLG8+cvcfFiIIMH9wW0gelbb71DXNw9du7cwNmzh2jYsB6tW3fKE3ynpqYxffqP/PLLj1y5chpXVxd69x6Kq2sFTp8+wLlzR5gw4TPMzJ69VQlw8+YtXn+9PSYmJvz55x/8889hhg8fTFaWNoiaPfsn5sxZwPTpk7h48TgdOrxBt279uHIlON/+kpOTad++OzY2Npw+fYCNG3/n2LGTDBv2UZ52Bw8eJTQ0nL17N7Nv35ZCz9erhpNTBkuWnKdx45JVcjcxk0rZ5q24Psils0jPmEF+OZAhwy+6I+N2HuLLTeepfb0LR2ss4pueXixq25Vw52NF6ogLQ0LCitZ4sofqIgg7+nCfZQRL1YmgI484+Ez/yc6vozJ3fNyHJpMsM3sSKvcAoSHdzgd5ZiKWsaeQNCrKhS3Dbt0RYke8Q+SKb7n15SBwfsjV0D7c+aExplEPce+6E6+aq7D9tfD1Gm6TFAREmVL5JwV3pBhiM+/k2a+r+4TCVEOjPlF8+/dOPti5hiyf3xGSNkJWq9UcvXj8hWYhdXXWMJQbhCFdJZ63Q4XREaN46LpIbw+QABwDOgPngW6ArRCiYelNz8jTmJkpWbLkJ3x9a1Czps8z+2/fvotKpaJbt05UquSGr28Nhg7tj5OTYz69aendW3s7cN26x4Hh0qUrqVatKo0bNwDgwIHDBAeHsmHDcurW9cfLqwrfffcNrq4urFmzMfc4lUrFTz/NpFGj+lSt6omlpSUxMTdp06YF1apVxdOzMl27dqR+/fyrPP7006/Y2Fizbt1SXnutDlWretKvX0/8/HwBmDXrJz77bAw9e3bD29uLKVO+pn79AGbN+inf/lauXE9mZiYrVvxMzZo+NG/ehIULZ7Nx41auXYvObWdhUYbFi+fh41MdX98aBZ6rVxELCzX9+t2gSpWSLS1QmOrpYqGvzVuOxKIYLhalIbEwZpBfPtzu+zPo0O9MXRNNu4tfEF7+CLPefp3vu9TjbJV1qGWqEvVvTg3cWYwvMTiLiaRyhnCpFaHU4T4r0WRfiKU41iOhyuPEhJDkqE2stKJfSYYyMQzzB4Ekl2+K2YMr2Iev4Had/3E/8AfSlw4gMfBjLM8EIVNncH9sHa6G9ufG7+1QW5lSYdThIucpLyPhPEzOkf5LtWmsJxGwaJPu7hOSBMGa35CZ5P2cZmXCpC/PE/RXefRwnDMYujprGMoNwpCuEs/bocLoiFE8dM0gX0SbNbYVQjQUQowXQuwTQqSU4tyM5IOvb3WUyvyzrwC1avnSqlVz/Pwa0717f37+eQn37mlVMDExN7Cycs3dpk2bBYCVlRXdu7/N8uWrAUhPT2ft2k252WOA8+cvkpycgoNDlTx9hIaGExl5LbedqalpbjCbw9ixIxk8+APatu3MtGmzuHq14FW4Fy4E0qRJQ0xMnl1s8+BBAnFx92jUqEGe55s0aUhISFi+/YWGXqVWLV8sLCxyn2vcuD5AnmN8fWtgampa4LyMFI2+LhYoZCDpLrHIySC/PBILBZoSFrAwUjpYp5an899Tmbb6Br2P/ky6aRJLWvdiQq/KBtEpm+CIC//DlxjcxG8IMoiW+vO32o1p9yvzQB2Sp31ShbZY39yD66lxOF6Zi9feN4nzGYWqTHnsojagkZkS6/dxbvuydw7zyL45KTtGkP5bX0ziE5AsY0kca0fUwa5gkb9/MpZ5n7/3MB/3CQli4+MI66Xi0RkNoyv2yHXBeHJ70hEjP0cFFJkkyi8yo31bvqnbkWO/V0FVQpmWPujqrGEoNwhDukqUhkPFyzTeq4JOK6OEEONLeyJGdKNMmfxXL+cgl8vZt28Lp0+f5c8/D7Fs2Sq++moShw7txMenOufPH81ta2f32KFv8OC+NG/+FsHBoVy8GEhKSir9+/fK3a/RaChf3pmDB3c8M6a19eNFiubmZjy9bnPSpK/o2/dd9uz5k/37D/Lttz/wyy9zGTCg19NdFZvirBV98hgLi8LPq5GiUZhJqPSxeZMkJKVCZ4mFKKbNm4QpSBqEyELS2binaOQaBWqZMUB+mTHNKsPrIe/TJGQYV9x2c8BvFlsafMaugG9pFDqElldG45BUpdj9yzDDniGUYxBJYh9rkt8jWnWN1ck16Wz9Pg58hBmepDg1IKTTaSqc+xqZJpM43zHE+Y4GISh3dTk3Gs3P7VORFodF/DnSrauiUZTBPuRX7HdsBvckpPQMyiUeYO15EFkWlJt/EdvfQ5ClZpHcuiLxY/xJFm7atC/kuk88ScYNwZ2FamL/UnN/s4YkzPN9bUmxj58vyFEhM13G6Von2D+3BkuGNmHz13Vo+X4oLYddxbJc6TjH5JDfa8sPQ7lBGNJVojQcKl6m8V4VjGWg9MDJKX+9YUHPvygkSaJhw3p8883nnDlzEBeX8mzYsBWFQoGnZ+Xc7ckAuWnTRnh7e7F06SqWLVtFx47tcXCwz93v71+Lu3djn+nD07NynnYFUbWqJ2PGjGDXro3079+LZctW5tvO378mx4+fQqV69laonZ0tjo4OnDx5Os/zJ06cpnp173z7q1atKpcuXSElJeWJ9mcACjzGSPHQt1AIaK3eNJn6lprW18VCe5yhdcgyjaLEt+yNPB9kyPCL6fBYp3ytK0dqLMzVKUc4nSihTlkG6toEp2l1/GFpEKP+hWCqEkkXkjlOhlUlrrVYRUzDudrgGLC8exRkCh5WbK91vABsordh+iiahMo9sIg7g0PIIu579iGs5nlCGoSTJtXDPCiKTC8b7sxrTljUIO5Obogy6AGVOm7H038NtsuCkAqQLikrSlSapqBulCkes0vmXGNqpuH1gRH878Q2Pvp5F1Xdo9kysQ7jKnfn9w/rc/fqi3F4MmLEEBgDZD24fTsJtTrxme327ZKVPzUkp0+f5bvvZnL27HliYm6wffsebty4pVMwOGhQH5YtW8WhQ8fyyCsA2rVrRb16dejatQ/79v3F9esxnDr1NxMnTuXkyTMF9pmcnMzo0Z9x5MgJoqO1x5w8eabA+XzwwXskJCTSs+dg/vnnAhERUaxZs5HLl68A8MknHzJ9+lzWr9/C1asRTJgwmdOn/2HcuA/y7a9fv3cxNTVl4MCRXLkSzOHDxxk5chzvvNOFSpXcijwnRnRHb4kFWicLfSvp6V8oRHucoXXIco0JwqhB/tfxpE75jQtfEl7+CDM7N+H7LvW1OuViymZ2JU9GgzZZIpBzLbkPznxFMke5KjUljPo8YB1C9vgzklquDunW3pg/uAwyOdbRO7C9toUUh9dILt8U1zOfkVShDQmVeyDkpqDJItOyIort1qQv6Uf60gGo7cyI/7wuV8MHcHNJa4RCRoXhB/H2XI7DlL+R30vLd75yS4nyo0p+RyUjRnC1Zxbylbd5LeoYoxsvp2HXcI4u82J8zc7M7dqCkCNOL0SnbMRISTAGyK8Y1tZWnDhxmk6deuLtXZdPP53AhAmf0Ldv4U4WAP379yIlJRVXVxfatWuVZ59MJmP37k00adKQoUM/pFq1uvTsOYjw8EjKl3cusE+FQkF8/H0GDnyfatVe4513BtCkSQNmzJicb/uKFV05fHgXqalptGzZkYCAZvz882+5Psljx37ARx+N5NNPv8bPrxE7d+5l8+aVBS6ss7S0ZM+eTSQkJFC/fiu6d+9H06aN+PXXH4s8H0b0Q99CIaD1QhZputq8aTXixc8g63dcUcg1JmTJ/1ue2a8SNqkuvH12ClNXx2j9lE0TWdK6F1/3qsJ+v5mkmT7Uua+H6jucSluGOvsuhZpMzqRtwEL9Ab7EUFEsRE0i16VeBFGFWGahFoloTCxJdmxA1V2t8DjYC49DfUl2bkKs3yfYXNuMpE7ngWcfsswdtAPJFFjGniTLzBEkGQhB+tIBAAhTOYn9qhN5tifX9nUmLcARp0ln8K6yDJeRB1GGPDD4OVQnC0K7q5CXhSoLFLx2U4m5bRYd2p5iVuQmOo6/TPgpR35o8wbfNnyL0+s8yFL9Z0onGPmXI4lX6LIuIMBTnD49K9994eGuVKtWfK2ZESMAoaGReHndfNHTeCnZ/nUyf85IYX66k87HhNZYgLm/M+6rHxejKaiSHkCdJUpifT/iVv0fdB4jnqXESEPwEddQUknn44ri+871KZNpy+jdew3Wp5EXhwYNV9x38affLMJdjmCWWZZGYYNpGTgG+0cehR675uFITqQtyQ2QAeSY0sR8KL2sFwAg0PCQXcQxi2TpCDJRFnuG4MAYrB8kYxF/jjTbGqQ6vAZCQ4V/JiBpVNz2/xqNqVaqYBu1iUpHB3GxbxxCkb922GzwitzHpqEPsJ93EZtVocjS1Txq7078R/6kNHfN1SkPNB1Q4OtanrmiwH1CCG5NVxO7VE1A2OOF42E9VSjsoMpC7ULrzDQ5J1dXZu+PPty9ao1thRTajAqh2ZCrWNgYJUpGnj8DTQeeE0Lkb6X1BC9P+TIjRoz8qzExA6EBdZZArtAtS6SVWOguU9DIzZDpafMmQ+t+YWgnC7nGxKhBfoXI8VP2i+5IjP15/qo5h8M1FnDIZz7+17rSKnAsVWIb5XtslOpUnuAYtFnkSNXJ3L8lZNjQERs6kirOEcsc4viJOOZhY9cNJ7txWPBadmMZivT7yLJStcGxEEjqdNxOjuJO7S+1wbEQuUHuk+RklAEYvILbC1sS+21D7H4JpNyiy3i0+4M0P3vuj6nNw3erYuWUlmdBXg5WTvlLM3JQxcHdRWrcpz0OI1QPBHIbMK/6eF4mZlk0HxpO0wFXCfzTlX0/+rBhfF22TanF64PCaTMqBMfKyYWOZcTIi6DAAFmSpEeg26oFIYRRiW/EyL8YlUoiLk5JcHBZHj40QS4XuLun4uKSjrOzboGlQqn9UczKALmOl96SUo7QcZEeaHXIxSkUAobXICs0pqhlRonFq4hbfB0GHVpJ5zPfc6jmPI5X/5XzVTbhEduA1pfHUftaF+Ti8Zs8afoFyGcpSpIVMP3Z58sQgAerqMD3xDGP+/xKorQRC9GQxZ8dJDnJjC72AbxuvZ2x68Hf8hg9yi8m08OFu7WzTaV0cO5JXzoAs8ErUDuYc29CPeI/qYPN2jDKzb2I65ADOE04xZpRF0h4zxe1nVmB/Yyu2OOZILoWF6kuD6Vuz8efq5SLgsxbAutmj9WbOW5BCds12AVF8/Gmm9yKsmP/vBocXFSNAwurUafTDdqPC8KzQf7WbS8TicmJLNy6kJFdRmJjafOip2OkFCnsZ2zUc5uFESNGXhgJCSaMGuXHzp3OmJtrsLPLJC1NTnKygtq1E5kx4wq1axe9EPVxgCxQWuiWQZb0WKQH2RnkYi7SK40McqaiZMVVjLzc2KZWoOuZH3jz3Nec8l7OwZo/srhND8olVaLFldE0Dh2CucqKpAI+HgU9n4MprrgynfJ8w32xjDjmkJykDVT3POhDU+ud7PUrz50Md66l1yCy9SbtgQVkj/MjJ0gGEGYKEgb5kDCwBpb7Y7CfewHnr0/hOO0sCf2rc//D2mR6PRv05ZdhtiWBa+pKgNZPPj1akLhfgySXsO8hy56mQJIkNCpBmRoSCTs0nPfKpMKn93hv6Qm6T77AXz97c2ixN+f+cKdyvXu8MSaIgC4xyBUvp/xz2/FthN8MZ/vx7fR/o/+Lno6RUqTAAFkIUbD4yIgRI68M779fG6VSTVDQX7i6Pl7IlpEh47vvqjJ8uD9Hjx5DqSzcztAkOwGlz0I9mVKBJk13mYI2g1zcRXqGDpBNyZKXrterkZcDsyxLWgSNolnwCC677+CA3yw2NRrHzroTaRIyDJhZov7lWOLIhzgwMve5dI0F4yK3464MQ42cmxmeLLJCr+AYAI06j+zCbPAKkCSS27mT3M4dZWA89vMuYrs0CLtfAnnUwYP4j/xJbeJS6Dh3KI8b2rLOQi2IW64mNVhQfpQcSS4h1AJJrj1eZiJRprqE13IZKVc0RI3MwryaGrsOqXSfcoEOXwRy/HdP/vypOgv7NKecezJtR4Xw+qBwzK1eHhlTTslmIQTHLh+jU5NOxizyK4zRxcKIkf84Bw86MHPmlTzBMYBSqWHSpFDCwixJTS3aL/VJiYWuSEq5XhpkIVfqnUEuNYmFWkmWUWLxn0Im5NS+3plPth9j/Oaz1IzuwMGahnPEkXj2cxad4c3NDE8AUjmnX3AMVDo6GM99HSl7+3Cu60XOBpBR055bi1tzNWIg9754jTIn71C51RaqNNyA9bqroMr/8xmHI7YkcKl+JsFvqkjYq8FxgAzbttqwIic4BsiME9yem0VqsAYLXxkmjhIZN7T7RJbAzDKL1iNDmRb4Bx9uOES5iims/fQ1xlXuztrP6nI/xiK/KTx3nizZbCzV/OqjU4AsSZKpJEnfSpJ0VZKkdEmS1E9upT1JI0aMlB4VKqRx8KADqalyVCoJlUoiLU1GQoIJGza44O2djCQVnRVWZFfq1scLWTKV6ymx0F+DXFoSC4Xa1Gjz9h/GPb4uQw6uYcraqOc2ZqhUl6s0J5HtCHQrUJVu7Y1F3Gm8d7Wg+h91sYtYjaTRZmWfzCxnOVsQ920DwiIHcuun5siSM6nYfx9Vq/2eb78J2LGBd3F6T075D+RU32qCfbf8L6RNHSU0GXDRX8Wleplk3haILO33hKSQUMULEv/UIEkaAjrH8OXBvXxzcid+b9ziz/nV+dS7K4v6NSXqbNFFqUqLnOxxTslmtVrNscvHSEwuWdlyIy8vurpYTAbeBaYBc4BPgUpAT+DrUpmZESNGngs//hjIoEF1WLvWFX//h1hYZPHokYJr1yw4etSeuXMvY2NTdBCbm0HWR2JhpkCjTwZZpiy2D7LG4D7IxkV6RsAuufCCQ+mKZMyyLA0yVgUxi3vMJUp6G6XwwpGxlGMAMsoUeMxd/y+JrTmWchGrcAqcTeVDfcn8+3PianzIverDnpFfiDImJAyrScJQX8ruuU65Hy/AjYLn5Dz0cVB8a3YWMlPyLUDi+pmCMj4SN79XU/FLOWUbafNz17/I4uERDaghvY+g8jwFDj3lVK57nxGrjtJjqgX7f6rO0aVenF5fmapNYmk3Ohj/jjeQyZ+fTvnJ7HEOOVlkoxb51UTXALkH8L4QYq8kSTOBbUKISEmSQoA2wC+6dCJJ0ihgIFATWCuEGFhAu4HAEuBJn5kOQojDOs7XiBEjOtK8eTxnzhxm/XpXzp+3ISlJQdmyWdSo8Yjvvw+iQgXdAsvcAFmPmFFS6r9Ir7guFgbPIGtMjRKLl5jPPst/kZyVFUzPx1midBB82bciTUKG0eLKh0z7wLXIOUkS+VadkyRwYhyOjCZBbCaOWdyQRnJbTMCe93FkFCaUz3PMiBE5fZkD72VvIKHhbIqc8hcmE+89mDjfMcRZlGHWjKUMtVmPtdwZs8ErePSWB4/e8sDaOYWHD56VOTxtBWfVVEZ6hHbyKYEasu6DdXMZmkyBzFTCxEHCaagc2/Zy1CmC2OVq7v6qptomE2xayojfpCZ+rQa7t2XIzbXfJ+XcUug1/R86T7jE0eWe7J9fg/k9WuBYJYm2o4Np0i8SM8viVT/Uh8hbkbnZ4xzUajURtyJKfWwjLwZdA2QnIDj7cTKQo0rfC+ju2A+3gSlAO7Sf2MI4JYRookffRowYKQZHj5YjICCRDz8s2a3inEV6ekkszBRo0nX/cRMKM+Rpj/SaV2n5ICvUSuMivZeY4jpLGBaJajfb8KffTA7UnI2mX/4Lzp6cU0G1u3Kel1Bgx7vY0oMUcYI45hDL98QxA1t648hYylCr8L6QEdT1Ik6Bs3EIWYRj8AImNXQnotx1didPopf1wjyZ5bl3tWv2V27+jYOhx+l62YnxW11J9XAmfrM/SZ0rg1xG2ddklM22ck7YreHhQQ1mVUxQVpRQPRAknxck7FTj2FdGymXBvTVqKk6QY9NSm022rCMjYkgWqjiQu+eds7mVinajQ2g9MpRzf7ix90cfVo1pwJaJ/rQcFkarEWHYVig9V5lJQyaVWt9GXk50XaQXA7hkP45AG+ACNCRvlrdQhBBbhBB/APd1nqGRImnZsgMffvjpi56GkX8p773nT0SENjuk0Wh/VHM2fVCYaTM++rlY6LdITyNTIulZKKQ0F+mpjRpkI0Uw7MAGJq+LoHnwBwbtV0LCkiZUZjM+XMWe4SSyiVCpNuG05iG7Cz0+rVwtrjdfQWDP6wT7f8A+m2sIBKeTFyFF/QKaxxeu6UsHkJicyNHIMwgJttd5QNCsABRxqbj12kPV6ispN+8iskePPw+unyso4yfjQq1MIkeouNpLRexiNXZva10uEnZqkBRQYdzjPN3DoxqsmkiYOGidMdKjBbEr1NxZ8Pg7Qq4Q1OsezTfHdzPh6G6qN7/Lrhk1+cSrG78MbEL0RVsDnmUj/2V0DZC3Aq2yH88FvpUk6RqwHPitFOYF4C9JUnz2wsCvJUnKN9stSdIwSZL+kSTpn/j455oaeC4MGjSSjh3fLbTNpk0rmTr1m2KPkZqayldfTaJq1TqUKeOMo2MVmjZtx9q1m3Tu4/r1GORyW/7550Kx52HkxRAWdoBatbSfHZlMeys3Z9OHYrlY6LlIrzguFqW2SE9jikpmzCAbKRr7Rx70OGk4t4unUVKFiszHlxhcxPekE0Kk9JZOx6osXFjimYVarl1lq5EEf8a+T831njhdno0sU/vdsGVx2GMHBzSs8IrgalA/Yta3R+ViQflPjuFdeRlOX5zA5Ib2Lo/HDAW1L5iiKCdh84YMj5kKnN+TI4QgbqU6j345M06Qcl6DmZeEvIxE7DIN4f1UxK9TE79BzfkamaQG59UAeza4x4cbDvNDyBZajgjl/DY3JtbrxA/t2nJxdwU0uq1jNGIkX3SSWAghxj/xeJMkSTeAxsBVIcTOUpjXUcAXiAZ8gPVAFtpFgk/P7VfgV4CAAM9SV+zHxm7k+vVJZGTcQqmsQKVK3+Dk9E5pD5svmZmZmJqaYmdXsivmESPGcfLkGebMmYavbw0SEhI5ffosCQkJBpqpkX8rWVkSGg2YmpaSi0V2qemcggJFURwXi1LTIKuVaORZaNAgMzpmGikh216bQPOgD+ApHbE+KLDDmc9xZCwJYoNOxzxU3+FU2rLcUtkqGWyvZEqvhy64n/kYl/P/I8ynF6cqrkBNXgeHTk06QRdPkrp4Yn72LuV+vIj93AvYz73Aw+5exH9UGwKccJ+SN9R4dEIgKcCmnSzXLzlhh4aMGKjwiZxHf2uI/VWN4yA5TkNkyEwlQrqoeHRWUKbGs6/BsXIyfWadpfOESxxZ6sWBBdX5sXNrnKs+5I2PgmjUJwpTc6PhlhH90NXm7fUnM7hCiDNCiNnAXkmSXjf0pIQQUUKIa0IIjRAiEJgEdDf0OPoSG7uR8PAxZGTcBAQZGTcJDx9DbOzG5zJ+TjZ5+vQfcXPzwc3NB3hWYrFlyw5q126MhUV57O09aNHiLWJj4wrsd8eOPXz++Vg6dHiDSpXc8Pf3Y8SIIYwc+V5uGyEEM2bMxcvLHwuL8tSq1YhVq9bn7q9SRat5q1+/JXK5LS1bdgBAo9EwZcoM3N19MDd3olatRmzblvfW3+TJ0/HwqIm5uRMuLt4MGPB+7r69ew/QrFl7ypWrhL29B2+80Y2QkLASnEUjT3PypB337pnmuy8kxJK1aysWuP9JnqykpysypfZrRddy08UpNS0rNYmF9pwYZRZGDMFe/6l82du96IY6IMOUcvTVqe2u5MlonrKMU0swr6E/wZ3/IdGtA9vUv8JTnztNlsTWxVdztcpprzlzc/UbXA3tz/3RtSm7+xqeDTfg0WozZbdHgebx94JFLQnzqhKpgdrg+MFONff/UGMZIGHVREb0+CysW8mw764NjkWWQFkRUoMEQlPw94uFbSZvfhzE9LDNDF9xFDNLFctHNuLjKt3ZPLE2D2MLLqdtxMjT6LpI7xDay9qnoyzr7H1FVxEoGQLQ84av4bl+fRIaTV7JtUaTxvXrk55bFvno0ZNYW1uxe/dGRD4i0bt3Y+ndewhTp35D166dSE5O5vTpfwrt09nZiX37/uKdd97G2to63zZffz2FzZu3M3/+DLy9vTh16m+GD/8IW1sb3nqrHadP/0WDBq3YvXsTtWr5YmqqDR7mzVvEzJnzWbhwFnXr+rN69Qa6d+/H2bOHqV27Jps3b2fWrJ9YvXoxNWvWIC4unjNnzuaOm5KSyujRI/Dz8yEtLY3vvpvF22/34sqV07ljGCkZQ4f68+23Ibzzzm00Gq3MIudflUrGzz974O39CAeHwgNBk2K5WGi/OkSGGpRFfx1pimHzBgoQUqlkkAGy5BmYqI0/vEXxvF0lrKwKHk8fHjtB5EWS4Oef9eurMIeiN+ijAAAgAElEQVSKb9dd5WDNuRzW4edO13NZ0HhIaiLogCMfE6U6lZs9zkFNJpGqk6Q6LOBayzX8HXcJlSb42TaZJ4C85axV7lbc/aEJcV/Vw3ZpEOV+uoR7911keNpwf3QtHvSthszShLL1ZAS1U2HXUUbCXg0VPpZTfrSc+/9n77zDo6i6OPzO9pDeSSW9J3SQJtKb0osgCjasSBFFaSIK8qlUUVAREEVQKQooghTpvSWQRhJIAoE0ShLStsz3x5IIksBuSCLgvM/DQ9jcuXMzZO+eOfM7v7NWj6EYnAfLUDobr4OgEMjfL+I4UECQCXd94qRQirQYfJZHnjxL/C5XtswLY8MCZzZkjqS5MJMnXsvGM0LyL5a4M6YGyALGIPWfOALXTT3ZjSy0AmNALRcEQQPoRFHU/WNcN+CYKIqZgiCEYPRarp007R0oKblg1us1gUaj5ptvFqBWqyv8fkbGJbRaLf369aRePaM/Z0REBc+kbmLRojk8/fQIXFwCiIwMo0WLZvTs2Z1OndoBcP36debM+YI//lhDmzYtAfD1rcfhw8f44ovF9OjRBWdno4G7o6MDdeu6ls89a9YC3nzzdYYMMd5AvP/+BHbv3sesWZ/x3XdfkZaWjpubK507t0epVOLt7UWTJg3Lj+/Xr+cta12yZAF2dt4cOnSU1q1bmHPpJCrB3l7Lvn2O2Ntryc1VodcLaLUy9HpjgJyQYMWVK8q7zqOoQqtpoSyDXKwDm4p/p29GVGiq4IMsIKCudh9khcG4Xq28GAsqvrGU+JvadpWorqD7bq4SAIsW3ftcLnkBPLn3M/4yYR5Tr2VFAbyOHLJZRDbHSRI60dcpEleWYs/g8qct/2Siy2kAZKX5OCUuwTVmLuqCcxRb55MZuYDcoOG3+SkbbFTkjm5I7uv1sVmbhNO8E7i/sROXqQe5/GIEylejcBxowfVjIm6j5Vg3kSEajE4XNm1kqH3+DoBz1ugpSja2sQZMkmMZx0Fo20xC22aycNVKDibv4fDx7zjYaCERnS/QdVQs4R0zzK63kPhvcMcAWRCEsj6KIvC9IAg3p2DkGHXC+8w43yTgvZv+PRRjwd8SjDZyYaIopmEsCFwmCIIVkAl8D8ww4zw1glrtcUNecfvrtUVERGilwTFA/foRdOjwGFFRrejUqR0dOrSlf/9eODs7kZaWTkTE30Hlu++O4d133+TRR1uRlHSCAwcOs2/fQbZv303Xrn158cVhLFo0l9jYBIqLi+nefcAtG5NWq8XHp3KT/Ly8PDIyLtKyZfNbXm/V6hE2bfoTgP79ezF//iL8/RvQuXN7unTpQM+e3cp/xuTks0yZMp1Dh46SnZ2LwWDAYDCQlnb7/4NE1XB2LmHx4nrs3OmITidDoTCgUIjI5SIajYHQ0HxcXe+efS2TWJgVIGuMW5CpVm8G2Q2JhSiaVUUoQ11zGWTJC1miltjQeCptT78KuFR5DgVOuDEJV97iiriSTGaRKjzLBfFdnHkdZ15GgWOFxxpU1kbP5LDXsD/3C64xs6i3byQeRyaTHfoSWWGvo7XyvC1YzhsYRN6AQOrsv4jjnOM4f3wEp9nHuDYoiNxRDSiu7wyAIBPQXRYxFILCxpgpNhTD2dE6PMfLkVvcPXtcEVcLrnIsbTsIIvKmS+jaqC97F7Xi0x6d8Iy4TOc34njkyRRUGqmqT+Jv7pZBLrNjE4Ar3GrpVgrsAb429WSiKE4Fplbybaubxo0Dxpk6b23h4zOFM2dG3SKzkMks8PGpuoOEudSpU3nHJAC5XM7mzWs5cOAwf/65g6VLv2fixGns2LGR8PBQjh3bVT725uI+pVJJmzYtadOmJePHj2H69E+ZMmU677wzFsONUuBff12Jt7fnLedTKk19CHErZRucl5cncXGH2bZtJ9u27eSttybxwQf/Y//+rVhaWtKz55N4eLizcOEcPDzcUCgUREQ8QmlpxX6iEuZz5YqSefOiee65tHuaR6kx38VCVi6xMC1AFuUaBEQEUYco3D2rXYaApkYlFhIStcFvTd5nc4OZMPzen4bIUOPIcBwYRr74J1nM5qIwiUvidBwZhgtj0BBUycEKrvj154pffywz9+MaM5u60Z/gGj2LK/5PcilyLEVOxieB5fILQaCwpTuFLd1RJV/DccEJ7JbFYf99PAXtPckZ1ZCCLvWwbCTjykbjZ07eHpGsb/So3AQ8xxs/a8wNjuHWLngG9BQ3msmnZ4Zz4EdfNs8NY8mIVqye3IiOr8TTbkQC1k7Se1riLgGyKIrPAgiCcA74VBRFk+UUDyNlOuP7xcWiMgRBoEWLZrRo0YzJk98mMrIFP/20junTIwkI8DNpjtDQYAAKCgoICwtGrVaTmppO+/YV12SqVMZg5eZOQzY2Nri7u7Fv30E6dGhb/vrevQfK5wfQaDT06NGFHj26MH78aNzdg9m79yCNGzcgPj6RBQs+pV27NgAcO3YSna7muyb9l2jR4jL29sYbDr3+bw0ygCgKiCIoFOJdE7byqrhYlEksTPRCNsiNQamgL0GUmR4gy1DXiA8ySAGyRO0xdVU826LmsLsa5xQQsKEzNnSmSDxNFrPJZQk5fIktj+PCWKxoi1CJLvq6awtSXH9GlXcW19PzcEr4Bsek78lza0dm5Biuefe4LaNc6m/LxTltyZzSHIfFp3H84iQ+vTZQHGKP9csNOSQGcNi7BLW3QJ1QgeBVxvd6VbPHe6L3lH823ezA0eYZA62fTiZuR102zQln7dSGbJgZSaunk+nyRixuwQ+fdayE6Zhq8/Y+gCAITQB/YKMoitcFQbAESv6pIX6YcXUdcN8FxDdz4IAxG9u5c3tcXZ05fjyG9PQLtwSk/6R9+8cZNKgfTZo0xNHRgdjYeCZN+oCQkCBCQ4ORy+W8+ebrvP32ZERR5NFHW1JQcJ0DBw4jk8kYMWI4Li7OWFhYsGXLdnx8vNFo1Nja2jJu3Ejee+8jAgL8aNy4AStW/MTu3fs5cuQvAJYt+wGdTkfz5o2xsrLip5/WolQqCQz0x97eDicnRxYv/hYvLw8uXLjI+PFTUCiqlrWWqJiZM/8uvpHLb/274tKDipHJBORKcwNk44kMZrhYgDFARml1l9E3nQc1YnVrkKUAWaKWqXstmKd2L6rWAPlmLAinHt/gzgyy+YIcvuCM0A4LsRGujMWegQhUfGNaauNLeou5ZDSailPCYlxPzSNwS0+KbIPJihhNbtAzGBR1bguWc95qTM7oBtj+nITT3OPUG70dD+f9pPZvwrUhQaiaG5+aViU4hluzx2UYRAPr96znma7PIAgQ1v4SYe0vcSHWls3zw9izPIC/vg6mfvd0uo45TcijmZJO+T+IqTZvroIgHAAOAT9gbD0NMBuYVUNrk6gCtrY27N17gJ49nyQ4uAlvvTWJSZPGMXRo5c1GOnduz4oVP9KtWz/Cwprx+uvjaN26BX/8sQb5jUhp2rSJvPfeO8yevYDIyBZ06dKHtWs34OtrtCVSKBTMnTuTb75ZjqdnKH36PAXAyJEvMW7cSN555z2iolryyy8b+fnn5dSvHwmAnZ0tS5d+T9u23YmKasnatRtYvXo5vr71kMlkrFy5hJiY00RFtWTkyHG8//6EO2qwJczn/HkNJ0/aUFRk3A4MBqPs4tw5CxITLTl1yppr10y7KVGoBfMkFpqbivRMoCyDbG6zEAFNtWeQlQYpQDaHytwjzHWVqG0qC4yqEjCZcg1MOV9l8wguWfzecDoF6ntrVqvEFXfeJ4I0vMRFGCjknDCUU/hxiY/RUbkDhF5tR2bUOGKeTCGl3QoMSmvq7X2FyB+8cT8yGUXhpfKx5cGyUs61IcEkHxzE2T/7UNisLv4Ld9Og4zLcX9qG+nSu2cHx+Y91FBw1kHwh+ZYnm2DMIiddSLrtGI+wazy3aD+zk1fTe/IJUg478b9OXXmv2ePsW+GHTitFyf8lhIqswm4bJAg/AJbAcIxtp+uLopgiCEJH4DNRFENrdJUm0rhxgHjgQMXx+pkznoSE+NfyiiQeNuLjkwkMfLgKBCdMCKOgQMGnn8agUonk5Sl45ZX6/PZbXQIDC4iOtmXOnBheffXsXed6xz2Lhv00DPrMtKinYFcqKR2X47d5KFbtfAFYsqRXpeMdE7/Fd+dwogclU2pjmlwIIJ6mKHAm4C7td80hwX0Hc55oz5j1Owi++Fi1zVtb1Lbtmim8/HLl3ytzijDVds2UcaaMMeU6mXota+qai4jEeWxla/1ZxHptRqm1oEXiMNrHjKbutcqfHpo+v4E8NpHFbPKF7chESxx5DhdGoeYun6uiiNWlPbjGzMIudT2iTMnlgKfIjBxDkUNk+bAym7gyVAlXcPzsBPbL45AV68nv4k3OqIZc7+B117sTbY7IsdBS9NfAupWA+yg5Dk/IEOTmBbilRXL2r/Rj89wwMuLtsHMvpOMrcbQbkYilvVSc+6AyXDX8qCiKTe42ztT2Tx2AiaIo/rO1WjJQuY2BhITEfU9Ojgpray0qlUhxsQwbGx2uriUMGXKew4d30r37JZMahUBZBrkKEotaySBLEoubqW3bterCFNs1U8eZMsaU62Tqtaypay4gEHahE2/8/gdTfjpF0+Qn2ReyhKlPhvBFl54kuP2FaIZc6vb5ZdjSg0C2ESIex44+ZLOQ0wSSQn8K2Ff5/IJAgVsbkjv/wqmBCeSEvIB9yo+Er4ki8PfO2KRvBlGkeMmw8j8ApcH2XFzQjoSUZ8l8/xE0J3Lw7f4rAY1XYrc8DuEOdQtKJ4HGySp8PpVTel4kYaCO4xGlXPxCj/666ddBZaGn7XNn+PDEr4z5dSseoVdZPbkxY/36893oZmQlW5t1HSUeLEwNkC2Aim6XnKGaP3UkJCRqFWtrHaWlxq1Ac8PmqLBQjoOD8S3v5lZCYaHpEgutGTuCzMwiPVFWpkE2b9uR1aAGWSuXtkCJ+wf3K+E8s3MJM1ak0ePoFJJd9zGnZztm9G3MwYAV6GX35gBUhwb48B0RpOLKO+SzjUShFQk8whV+RqTym90S20DSWn1O9OB0zjedgcWVUwT90ZXwNZE4xX+DoDO+l24OlPVOFmS/25TEpOGc/7oDAJ4vbCUocBnOMw4jzymq8FwKGwH3NxQ0ilMRtEKBwlHg7GgdR/1KSZ2go+SCOfUVUL/bBd7a9CfTDq+nSd9U/vo6iPFhfZjfvx2Je10qvdmSeHAxNUDehVFeUYYoCIIcGA9sq+5FSUhI1B4NGlwjPt6aHTuMzV42bnTl/HkL6te/BoBabUCnM+3RpEJdtSI9U23eDDe6kdwPGuQHPYMs8XBjU+TKE0fe56MV6Ty18yu0iiKWdhjKxMG+bK7/MddV/3wgbB4q3PFgBhGcx0v8HD2XOSsM5DQBZDIHPZWnxfUaBy41eJeYJ89xtu23iIICn90vELWqHm7HpqEoygZuDZRFtZyrw8JIOjqYs7/3ori+E65TDxDsvwy313egSqz45xEUAk4D5ETtURGxU4nNYzIuzNZzLKiUM89qKThunvexd/0rvPjNXmYlraHH2zEk7HFhRrtufNC6Owd+9JF0yg8RpgbIbwMvCoLwJ6DGWJgXC7QC3q2htUlISNQCQ4akExGRx6BBTWnc+DFeeqkhjRpdpX//DADatMmhSRPTPkyVGgGtGQFyWZGewdQMstwYIAsG84JSWQ34IJe1l5YCZIn7GZXegjbxLzLlp9O8tmkjrteCWffIeCYM9WJVq5FkW6fc0/xyLHHmVcKIx09chwpvLghjicGL87xJKZX7q4tyFblBzxDb9zgJ3bdy3akJHkffI2qlN/V2j0BzNR64NVBGELje0ZvUDb04c3wI1wYFYf9tHEER3+PdZyOWO89Xqp2xaSEj5EcljWJVuI6Qk/uLgejmWk51LuXy73pEg+l7l51bEf0/OM7s5DU8Pf8A16+oWfR0W8aH9mXTnDAKr5luQylxf2KqzVusIAhRwCtACaDB2Pr5c1EUL9bg+qqVqtrESEiA8ffnYUQuh48+iuWVV86SmGhFeHgebm5/B319+5r+FjfXxeJvH+Sa1iDXYCc9KUCWeACQISMyrQeRaT1IdzzBtsg57A79kp1hX1A/tRedTo7DP7NllecXkGNHb+zozXXxMFnMJot5ZDEPe/rjwptY0rSSgwXyPTqQ79EBzZU4XE/NwfHMdzjHf81Vr+5kRo4l3739bRZxJeGOXPiqA5c+aIHjomgcvozBptNZiho6kzOqIdcGBIBSftvpNH4CfnMUeL8nJ3Oxnotf6InvrcMiSMBtlBznp2TI65gWK6gtdXR4OYF2IxI4+ZsXf8wN48fxTfn1w/q0fe4MHV+Lw9nnP91C4oHFZEPZG4Fw7bWMq2aUSj3FxaVYWEgWYRJVQ6vVI5c/vK1IPTyKcHIqpbBQTnq6BpnMqE+2sTHd5rzqEoua1yBLRXq3YmNTuaNCTVBdDg6CULnzhLmYMpcpY0y9lqaMqw13Ea/cBgz/61t6HZrBzojP2RW6iBO+6/DNbE6H6LE0PNsXuVh1v3lLmuLLSjz4H1l8Rg5fcUX4EUuxNa6MxZaeCNweuAIU24eS2uYrLjSZjnPcQlxiPyf4944UOtQnM3Isl/2fRJSrbguWs957hOy3m2D3QzyOc0/gNXwLdSfuJffV+lx+MQKD3e2f/Qo7AY9xCtxGycn92UDGPD0pr+lImwJ1X5JT9xU5KlfTfrFkMmj4RDoNn0jn3DEH/pgbztbPQ9nyWShN+6bSZXQs/s1yqnZBJf4V7vgOEAShDvAJ0BtQAluBN0RRfOD+lx0dL3PhghIPD3c0GpWUSZYwC4NBJCsrBxub+7zEv4pkZGhYutSbrVtdyMw0fpDY22uJjLxG//4ZdOyYbdI8So3A9cum30SUZZANNZ5BrgGJRZkPsuzBDJBr28qtuhwcbrZyu1dMmcsUpwtTr6Up42rTXcS+0IPeh2bQ7dhE9gcvY1vkXBZ3GoRDfj3ax7xBq/gXsNBW/Y5JhTeefIIbk8kRvyGb+aQIfVGL/jgzGkeGI6fihj86C2cuNprCpai3cUxagWvMbHx3DsPj8DtkhY8kO+Ql9BoH4O921qKFgivPR3Dl2XCs/jiH07wT1J24D+cZh7k6PJSckQ3Q+tnedi6ZUsB5iBynwTLydotkzNVzfoaeC5/qcR4iw+0NOZYRpipSwafRZV5evpuBM46y9fMQdnwdzKHVvgS0yKLr6NM06pmOTP5wPpF8mLjbLeL7GIvzVmB0qxgMLATu31ZylWBtXQJkkpGhRaut+M5VQqIyBAEsLIpxcCj4t5dS7aSmWjBqVBTZ2WpGjkymXr1CVCqR3Fwla9Z48Pbb4UyenECfPneXWihUAjpzXCw0ZrpYlGmQpQyyhES1odZZ8tjp13g09mWi621ga9RsVrd8k42N36d1/As8dmokTgU+VZ5fjg2ujMGFkVwV15HFbM4LI7koTsGJETgzEhUeFR4rKjTkhDxPTvBz2JzfgmvMLDwPT8Dt+IfkBj1LZsQoSmwDyzPKmue+BZlAQXdfCrr7ojmRjeO849h/dQqHhTHk9fQjd3QDClu43fbYQRAEbB8VsH1URlGigYzP9GQvN5C1zIBdJwH30QpsOwomJ9gcPAsZ+NExnpgQzZ7lAWyZH8aCQe1w9s2n88hY2gxPQmP1n2lE/MBxtwC5L/C8KIqrAARB+B7YKwiCXBRF0z7R7iOsrUuwtn5gJNMSErXC7t2O5OUp2Lt3123f69w5mwUL/Fi82Me0ANlciYVCBjKhFjrp1ZwGWSsFyBIPCTJRToNzvWlwrjepTkf4s/4stkfOY3vkPBqlDKBD9Bh8s5tVeX4BBfYMwJ4BFIj7yGI2mXxCJrNwYDAujKEODSs5WCDPqwt5Xl2wuByDa8wcnOK/xjn2C67W60lm5FgK6ra5TXpR3MCZC0s7kzm9JY5fRGP/9Slsf0mmsKkrOaMakNc3ABS3Z4ctgmT4fybDe6pI5tdGnXJsDy0WYQLuo+U4D5YhU5sWKFtY6+j0WjztX0rg2K/ebJ4XxoqxzVn7fkPavZBAp9fjsfcorNI1lag57vbMwAv+bvsuiuIhQAe41+SiJCQkag+5XESvN270FT1OvnJFiYWFaffDCrV5LhZg1CGbKrEQ5VXTIAuoEYVSRKpPQy4gINcr0Uk+yBIPIfVymvDCtpV8+MNZOkSP5ZTX7/yvb3M+6dma4z7rMAj3liOzoiV+rCacJJx5jausJV5oRCLtucZvd3yvFjlEcq7tEqIHp3KxwQSsLu0hZGNbQn9pikPSSgSD0ev5ZvcLnbsVmR+2JCHlWTLmt0V+pRjvoZsJCl2O49zjyPIq7oyndBTwfEdB4zMqAhYrEOSQPELH0YBS0qfr0OaYvt/JFSJN+6UyadcmJu36nYiOGWyaE864wH4seqYN5447mHEFJWqauwXIcm5vEKLDjOI+CQmJ+5tGja5hZaVn6NDG7NvnQEKCFfHxVuzc6cj48eFs3erM88+fM2kuhcY8FwswNgsxVWJhkFfNB1mG8Tixwn5HVUehV0sZZImHGofrXvQ7+DEzV5xnwL45XLW8wJdd+jJlUBA7whdQrLg32ZkaX7yYSwTn8RA/poQzJAuPE0sYOXyFgYobgQDo6tQlo+mHxAxJI7XVQuTafPx2DCFilT+u0Z8iL7kK/MNP2VLJ5ZejOBMzlNSfu6P1ssbt7T0E+y2l7vg9KFMrFnvL1AIuz8ipf0RJ2CYllg1lpL+v56hfKcmvaSmMN+/mO+CRbF5buZOP49bR8bU4TvzmydTmTzCzU2eOb/DC8PDWgz8w3C1AFoDvBUFYX/YHo8Xb1/94TUJC4gElOLiAL788jlptoH//ZjRp8hjNm7dl4MBmnDplw7RpcXTrlmVSpyilBrTFZmaQNQqTbd7E8gDZ3Ayy8bjq1iEr9RpJg2wilblj3Py6KWOq83y1Oc/9ej5T0Wit6RAzmmmrzvDilp+xLnbmx9YjeXeoJ+uavcPVOhn3NL8CO1x5iwhS8BFXIMOSNOElYvAigyloyaz0WIOiDtlhL3NqQBxnOm+gxMYfr4NvEbXSC6/9o1HlnwO4tZ21XEZ+L3/Obu9H0v6B5HfzwXH+CYJCluP51B9YHL5U4bkEQcCug4yw9UoanFDiNERG1nIDJ6K0xPXWcu0vg1mWoM6+BQz+5AizU1YzaOYRslKsmdevPRMie7NtUTAlhVLN1L+FcKf/SEEQlpoyiSiKz1bbiu6Bxo0DxAMHZv3by5CQeKDR6QR0OqG87TQYpRem1KWseyefXQsLmXPN1eTzxQV9hlVrb7yW9AJgyY2/K0QUabJYRkbDyWQ0mWbyObL5gnThNSLFSygxbW2m2G2985QnYee78MzOb0xey8OGqbZktWFfJlG7pLgcYGvUbI77rkEQZTRNfpIO0WPxzq1ER2wGIiIF7CaLWVxjAwJKHBiKC2OwIOKux9fJOYZrzGzsk39EwMAVn75kRr7JdddHbhmnee7b8q+V6fk4fH4Sh8WnkeeVcr2VGzmjGpL/hC/IK88nlmaJXFqk59KXenTZYNlAwO0NOU4DZchU5jlm6bQCR9b4sHl+GGePOGHlWEy7EQl0eDkBO7fKs+kSpjNcNfyoKIpN7jbujlKJ+yXwlZCQqB1EERQKEYVCRBSN/5bJTPeYVaiqILFQma5BRhAwyNUIVSjSA8wq1DPFbkuhV//nM8im2pLVpn2ZRO3gl/UII7b+RLZ1CjsiPmNvyGIOBn1P8IV2dIx+k/C0bshMbth7KwIC1jyKNY9STCJZzCOXpeQKS7AWO+PKm1jTCYGKN6dCp0acbfc955vOxCV2Ac5xX+JwdjUFLi24FPUmV+v1Bpn8FvcLrZc1mTNbkz2xGfbLYnH87CT1Bv5Oib8tuSPrc/WZUAxWqtvOpXIR8J6iwOMtOTk/GP2Uk57TkTYJ6r4mp+4LchT2pm2iCqXII0+epfmgs5zZ58Ifc8LZODOKTbMiaDE4hc5vxOIVebVK11TCPKr2myshIfFQ8s8GCTIzdwilBkQD6LXmNQsx1cUCjDpkWRVaTQMYqtvJwqB+YH2QJSSqC+d8Pwbun8NHK9Lpe+BjsmzP8Hm3x3l/YBg7wxZSKr+3zKeGILz5nEjScRM/pIhokoQuxBFJDkvu+L7WWnlyodlMooekk9ZiHoqiTAK29ifyp0BcTs1DVpoP3Cq/MFiryB3ZgMTYp0n7oSt6JwvcR+8iyH8ZrhP2ojhfse5abiHg+rycBieUhK5XYBEikDZRzxHfUlJGaSlONmNfFCCoVRZvrN7B/2LX0fb5Mxz82YfJjXvxSbdORG92N0n2JlF1pABZQkKi2lDcsD0yr5ueArHU9Ip4Ua5GMMdsmZszyNWtQZYyyBISZdQptaPzybf4cGUKz21bgUZrzco2rzLhKW/WN5nMNYuKdb2mosARNyYSwTnqicsQUJAmPM8p6nGRaWipvKGRQWlFVsQbnBqYSFLHtZTWccd7/2iiVnrhefBtlAXp5WPLdcoKGXn9A0nZPYDkXf253s4Lp9nHCQ76Fs9hW9Acr/h8gkzAvquc8D9U1D+sxLGfjMzFBo6FlRI/QEveXvN0yi7++Tw97yCzU1bT/8OjXIi1Y/YTnZjYoBc7lwZQWiyFcjWBdFUlJCSqjbIAWWtGzCjTKDCY6GIBYJCpzc4glwXI1Z5Blor0JCRuQ25Q0ixpCO+sO8Sbv+7CL7MlmxpNZ+JT9Vje9nkuOMTc0/wy1DgyjBCOEyD+SR0acVF4j1N4k8ZLFBN/h4PlXPXtQ0LPPcT1OkCeZ1dcY2YTucoP3+1PUSf7SPnQm90vih5xI31VNxLjnib3lUisN6QQ0HwVPp3XYf3bWTBUHPBa1pcR+I2SxkkqPMfLydtt4FQ7LdEtteT8pEfUmR4oWzmU8vjbp/j0zBpeXLIbhUrP0pda8QubKfEAACAASURBVKZ/f379MIq87NvbaUtUHSlAlpCQqDYURiUDOjOcLMyVWIhydZU66UH1Z5CNNm+SD7KEREUICAReasOrm39l6qoEWsW/wGH/lXwwIIr53btw2usPRKquExAQsKEjAfxOqHgaB4aSy7fECqEk8Tj5bL/j/NddmpPSYRUxg5LJCh+JXdoGwn5pSvCGttimrjfqxeCW5iNaX1suzXqUhJRnuTizFeqkq9Trs5HAqO+x//oUQlHFe5nKTcB7moLGKSr8PlOgvwaJQ3UcDSnlwhwdujzTr4NCZaDV0BTeP7SR8Vs249c0h3XTGvKmf3+WvNyCjLjb22lLmE+t+hkLgvA6xtbVkcBKURSH32HsGGA8UAdYDbwiiqKUqpGQqCE2b3ZBqxV4/PHK7ZTuhuJGxbY5Vm+CWoEh13SNokGuqUInPfM1yDY2lbsulKHUqylSXTNrLZXxyisVN2oRBFi4sPbnAdOcJ0y5TqaOM+V8khvGg4lrXiCD93xOz8MfsCtsEX+FL+Cz7t1wz42gY8xYmiYNRqnXVHl+C8Kox9e4M50ccSHZfMEZoQMWYgNcGIs9g5Bxe4EdQKl1Pc63mM3Fxu/hFP8NLqfnE7ilF8U2gWRGjiY3cNhtHfoMdmpyxzYid2R9bNck4zT3OB6v7cB1yn4uj4jk8iuR6Opa3nYueR2Bui/JcX1BxpXfDGTM15M6Xs/5D/W4PCfH7TU5Gh/TCvoEAUIfu0ToY5fIiLNly4JQ9n7nz64lQUR1O0/XUacJbXfJ5CJriVu5o81btZ9MEPoCBqALYFFZgCwIQhdgOdAeyADWAQdEUXznTvNLNm8SElWne/cW5Ocr2L17990HV8LRn4pZOvQaE0844hZm2v136qCfKY7PIfjkK+Wv3cnqLXRdU7QWLiR1/c3kdV3nEAlCc/zFjdjSw+Tj7sYXXXpxxSqNiWuO3/NcL79c+fcWLar9eap7ruo6X22vSaJm0MlKOeK/ij/rz+KCYzTWhS48dvp12sa+glWx0z3Pb6CYy3xPFrMpFuJQim748QuWmNAq26DD/uwa6sbMwjL7MDq1PdmhL5MV9jpay1sbCZfbxIkidfZk4DT3ONYbzyIqZVwbHEzOGw0oibzzz1NwzEDGXD25qw2IIjj2luE+Ro51M/Mf8udlq9nxZTDbFoWQl2WBV9RlurwRyyNPnkWhkrqPgOk2b7UqsRBFca0oir8AuXcZOgz4RhTF06IoXgE+wJh5lpCQqCFUKgMlJfe2JShuSODutUjvued+rXS8Qa6uQqOQmtIgS530JCSqgsKg4pEzzzBp9QlGb9xKvewmbGg6hXef8mJFm5e4ZHcHHbEJyNDgxAuEcgp/cRN1aIqGYBMPVnDFfxBxvQ4S/8Ru8t0eo+6JmYT+XA/HQ70xXF1dPrQ8sywIFLbxIG3N45yJGcqVZ8Ox/ekMgY1XUq/Hr1htSa340Q5g1UhG0HIljRJUuI+Sc3WrgZjWWmIeKyV3rR5Rb/p+auNcQq9J0XyatJpnv9yLQSew+IXWjAvqx4aZkRTkSjplU7lfW0aHAzd/Qp4EXAVBcBRF8ZbgWhCEEcAIAG9v59pboYTEQ4ZGo7/nAFmpKSvSM1ODbEaRnlgFH2RZFXyQTUGpl2zeJCTuBQGBkAsdCLnQgQy7WLZHzWV/0LfsDvuKiNTudIoeR1DGY5X6Hd99fhm2dMWWrlU4WKCgbmsK6raG/N2c1z2NoN1AnvpX7LId8S/5kkKPPrfJL0qD7Ln42WNkTW2Ow9encFgYg8/j6ykOcyB3VAOuDg5G1Nwefqm9BHxmKvCaKCdzmZ6LC/QkPKlD7QfuIxW4DJMhtzLtOqg0Bto+m8Sjw5OI2eLOlvlhrJnSiA0zI2n9TDKdR8ZSNzDf/GvyH+J+LdKzAm4W9pV9bf3PgaIofiWKYhNRFJs4Of3LvTglJB5g1GoDpaX3mkEus3kz/Riji4V5RXrma5BrJkCWGoVISFQf7lfDGLrrK2asSOOJw++T6nyEOU+0Z3q/hhwIXI5OVvqvrEtPAXHWo9DaP4Kz3W7aJcxEUXIdVWJ/wldH4BT/NYLOWEdxs5+y3tGC7HeaknhmGOcXd0SUC3i8tJ3ggGU4Tz+EPLvi2gu5tYD7SAWNYlUE/6hA5SJwdoyOI76lnHtXR8l58/yUo7pkMO63rXx47FeaDzjHriWBvBvRh3n92hG/y1XyU66E+zVALgBujnbLvpZudyQkagi12kBxsfye5qiyxMLMRiHmu1iUFelVs4uFQQqQJSSqG5tiF3ocm8KMH1IZuvNrDDIdy9oPY+IQX/5o8BHX1ZdrbS0iItl8hp6r+LIKlaollxqMJ9+jOwlN2mGQa/DZPYKolfVwP/oeiqKs8mPLAmVRJefqM6EkHxnM2T96U9TIBdf3DxLsvxT3V7ejiq/45xHkAo595ETuUhG5W4ldBxkZc/QcCyolcZiWguPmaYo9I67y/Nf7+DRpNY+/E82ZfS7M7NiVaS17cGCVLzqtVM13M/drgHwaqH/Tv+sDmf+UV0hISFQfxgC5eiQWZtm8qcztpFd1DfL9bPNWWaW5uRXo1TUP3O5EcbfX7xVTzlfba5L491DqNbSOf4HJP8fw+u+/43YljF+aT+Ddp7xY2fo1smySanwNOrLI5nPcmX7Ta5eRCw5g8zhxfY6S0GM7BS7NcD82jbCfvKi360U0V2LLx5f7KQsC19t7kbq+J2dOPMXVIcHYfRdPUNQKvHtvwHJHeqU6ZevmMoJXKWkUr6Luq3IubzAQ3VzLqY6lXN6oR6zEh7ki7OoW0+/9E8xKXs2wz/dTlKdk0TOP8nZwPzbNDuf6VWXVL9hDRG3bvClunFMOyAVB0AA6URT/+em4HFgmCMIKjC4Wk4BltblWCYn/Gmq1gZKSe80gl9m8mX6MoJYjag2IBhFBdvcoTpSZr0GuySK96sogm2vBVtPzQO3bpplyPsnK7b+HgEBEejci0rtx3iGarVGz2RuymF1hC4k614uOMWMIuNimyjrlO5HLUmRY4cDg8tcKOY6W81jTDgSBfPd25Lu3Q301gczr/ZEVLaX1r4spcu1KZuRY8jw6giBQvGRYuetFSZgDGYs6kPlBSxwWReO4KAabLr9QFOVE7qgGXBsUhKi6fT/W+Aj4fqrAa7KczCV6Ln6uJ76vDk2ggPsbcpyfliGvY9p1UNfR0+7FRNo+n0j0Jk82zw/jx3ea8OuH9Wkz/AydR8bh7FtxW+3/ArWdQZ4EFAHvAENvfD1JEARvQRAKBEHwBhBF8Q/gY2AHkAakAu/V8lolJP5T/FsuFrIbxSqmtpsW5eZ30qu5Ij0NerkWA5J9koREbeB5OYrhfy1j+opUuh6fQFLd3czq2ZaZfZpz2H8Vepm2Ws9XTBy2PFH+7xJSyeMPQIE9gwDKm5GU2AVj7XGAy769+P5pDYnuuwna1JmwtfVxTFyGoC+5RaMMoHe2IHtycxKSh3Phy/YIWgOez28lKPBbnP53BPnlirMNClsBjzEKGsWpCPpOgcIWUkbqOOpXStoUHaWXzNiDZdCgx3nGb97C+wc30KhXGtsXhfB2aB8WDGpL0sF7t917EKltm7epoigK//gzVRTFNFEUrURRTLtp7GxRFF1FUbQRRfFZqUmIhETNotHo0WplGO4h1isv0is1Q2JRFiCbKLMwapDNzSArQJRXewZZqTNqmyUdsoRE7WJbVJdehz/kox/SGLJrEUWqq3zTcTCTnvTnz6hZ1dbAx4o2lJICgIieXJZQzGlceB0BOSL68sy1iAE5lvjI1xAsj+d0fRdWDHMj164Q353PErnSB7fj05EXG9WiNwfLokbBlWfDSTo+hHPrn6AkzIG6k/cT7LcUt1F/oUq6WuH6ZEoBp0FyIvcqidiuxKa1jPP/03M0oJQzz2u5HmPehl6v4WVGLN3Dp2fW0P3N08TucOPDNj34oE03Dq2uh17339Ep368aZAkJiVpGozFupPeSRa6Ki4WgNgbIpjpZGDvpma/7laGpfhcLgzEzLbWblpD4d1Dp6vBo3EtM/TGeV/9Yj3OeP2tajOOdpzz5ucVYcqzP3tP8lrSgiFPE0ZgkOpPH7zjyHDZ0AUDgZhnE38GjmnpoCMegciWx/RwSu22mwDkCjyOTiPrBC+89r6C+mlA+vtwqTiZQ0NWHc5t6c+bIYK71D8R+8WkCw7/Du/9v1NlzoUKdsiAI2LSWEbJaScPTKlxfkJG7xsDJxlpOdyvlyh96zGkMZ+9RyIDpx5idspqhcw+Sn6PhiyGPMT6sD5vnh1KUf7+6BFcfD/9PKCEhYRJqtVHiUFIiw8Kiamlk5Y1OsWZJLNTGDxhTvZDLbd5E0azKMwF1jRTpgZRBlpD4t5EhIyr1CaJSnyDN6Rh/Rs1iR/hnbI+YR4Nzfeh88i18s5qbPa8F4YSTQA5focAVS5qjpG6FY8syyVdZTxazAfBjLWrBlzxPOOQ5Gdvip2h+UIVTwhJc4hZx1ftxMiPfJN+t7W1+yiVRTlxY3JHMD1rgsDAah69O4bc+hcLGLuSObsi1vv6gvF2nbBEg4DdXidcUkcyv9VxaqCeupw6LUAH3UXKch8iQaUzbOzVWOjq+Gk/7lxI4tt6LLfPDWDmuGb9Ma0Db58/Q6fVYHL0Kzb2sDwRSBllCQgIwFukB91So93eRnnkuFgCiiRlkUW4MSgWDeVpDGerql1jojXcEUgZZQuL+wTunEc9vX8H0lWfpfPIt4j228r8+j/Bxr5Yc812DQTC9MVEZTozAjl4oqUsmn5LFZ+XfK9MgA1zmBy7wFhrC8eMX1PgCcJEPESkmT5PKhrbr+fPpqWQ0moJl1gGCf2tH6C9NcEhaUb6v3Sy/0LlZkjWtBQkpw8n47DHkeaV4Pb2ZoJDlOM45huxaxfua0kHAc7yCRokqApYokKkg+WUdRwNKSf9AR2mWGYkMuUiTPmlM2PEHU/b+RmSXC2yZH8pbQf1Y9HQbUo44mn1N73ekAFlCQgK4OUCu+rYgv+EOZJbEokyDbGIG2VAWIFfByaImGoWAlEGWkLgfsb/uSZ9DM/loRTqD9swnzyKTrzr3Z8qTgWyLmEexsmqtFax4FAUugDE4FhAQ0XKJmVxgPM68jgcfo8AOAC2Z5PAFnswlmN348TNZqp840diZ6MFpnGv9JTLtdfx2DCVylS91T36MvORK+fnKMstiHSWXX4rkTMxQUtc+TqmfLW7j9xLsu5S643ajPJdX4XplKgGXoXKiDikJ36zEqomM9A/0HPUvJfkVLYVx5j0x9Guaw6srdvFx/Fo6jYzj5CZPprV8nI86dOHYei8M+odDpywFyBISEsDfAfK9eCELgoBCbZ4PsqxMg2xGkR5QJS/k6m4UUpZB1kkZZAmJ+xaN1pp2p0cy7cdERmxZjU2hGz+3Gs27T3mx5pG3uGyZbtZ8ljTD4YaDhYBAKedJYQDX+A033sOFkcixLB9fwF5EdGTyP7RkYk07QjmOE88hKizICR3B6QGxnOmykWLbYDwPjSfqBy+89o1ClWcsELzF/UImkP+4L+f+7EvSwUHkP+6L4xfRBIUsx2vwJiwOXqpw3YIgYNtORugvShpEK3F5Wkb2CgMn6muJ7aXl6jaDWTplp3rXGfzxEWanrGbwJ4fJSbVifv/2vBvZm22Lgim5/mCreKUAWUJCArhVg3wvKNSCeS4W6ipKLMzMINdIkd6NDLJWIQXIEhL3OzJRTqOz/Xj71728vW4/4eld2RY5h0mD/fim/RBSnY5Wad5iYikmnnoswYkXAKOjRRk2dCGCc6gJJokuFBOPiIiMOoiIlJBKrvAtZ7xTSOyxjdN9j3PFpy/OcQuJ/CkQ/z/7YXVpb3lx3s3BcnFDF84v70JC4jByxjTEamsa/m1+xu/Rn7FZmwT6irPDdUJk+H+hpHGyCq/35Fw/aiC2m5aTTbRkfafHYMYebmGjpcuoWD6OX8urP/yFpUMJ373xCGP9+rN6UkOuZFhU6br+20gBsoSEBFA9GmQweiFrqyCxMJhapCczBqVVySDXhA8ySBILCYkHDb+sR3hh2yqmrUzisdOvE1NvIx/1a8KsJx7jRL1fzfI2t6EzoZxAQyAixn1MQIaBUgBk1EFGHbyYhwo/CthTXtCXw0LOMYTL/MAVVnGaIC47qjjXbjkxT57jUtTbWF/cQciG1oSsb4F98k9g+DuZUCa/0HlakflRKxLOPkvG7EdRZBbi/eQmgsK+w/GzE8jySytcu9JZwGuigsZJKvy/UiDqIel5o075/Ewd2sumB8pyhUiz/qlM3v07E3f+TkjbS/z2SSTjAvvx1bOtSTtpb/Jc9wNSgCwhIQFUj80bGNtNm+NioQlxwmtZbzShppnRl0ksqpJBrm6JheKGD7JWJgXIEhIPIk4FPgzcP4ePVqTTf98scq3Psqhrb6YOCuGv8M8pUVw3aR4ZN/alG7ZvBoopYBd68m5olI1BrY6LlGKUdFzjD3JZigNP4c9vBLMXDaEUchAAraU7F5p9RPTgdFJbLkBRnIP/9kFE/hiAa8wcZKVGzfHN7hcGKxWXX69PYuzTpP3YDW1dS9ze3E2w31Jc39mL4nzFnfFkGgHX4XIaHFcSulGJZZRA2hQ9R/1KSR6ppeiM6TcMggCBLbIZ+dNf/C9uLe1fSuDoL95MadqT/3XpzMlNHvfkt19bSAGyhIQEUD1FenBDYmFGvKhwtsR+SCRKN2uTxpdJLMztplczGeQbRXqSxEJC4oHGotSWjjFj+WBlMi9sXYVFqR2rWr/OhKe8+aXpRK7WyTBrPgPXyeQjzjIEA4UIKLjMSgwUYUMnAC4yFWs6YscAZKgQ0aHEkyJO3SLRMCgtyQ5/jVMDEkjqtI5SK2+8Dowl6gcvPA+MQ5WfeluHPuQy8voEcHZnf5L3DKCgkzdOc48THPQtns9sRnMsq8J1C4KAfWcZYRtV1D+qxGmgjKylBo5HaInrq+XabvN0yi5+BTw1+zCzU1YzcMYRMs/YMKdXRybW78VfiwMpLbq3J5Y1iRQgS0hIAMZOelBNAbIZRXrmUtUMslADNm/ljUKkDLKExEOBXFTQJHkQ76w7yLhf9hBw8VE2N/yIiUN8WPbYMM47RJs0jwJH/NmIAkdO4UcyvUnjJRwYhhWtucxKAOwZjBJnwNjx8zr7UOCCgOwW+zgAZHKu+vQm4YldxPY+zDXv7riemkvkj/74bXuSOtmHAW4Lloua1SX9h24kxj9D7mtRWP92loBHfsS341qsN6SAoeL92jJSRsBXShonqfB8V07+AQOnO2iJbqEle6Ueg9b0fd7SvpTu407zccIaRizbhaqOnmWvtuRN//6se78+eVkak+eqLaQAWUJCAgCVqszF4t41yOYU6ZlLeQbZTA2yrCZs3spaTUsZZAmJhwoBgYDMVryyZR3TVp3h0diXOe63hg8H1Gduj06c8tp0V52yDAt8+JYgduPESwSzH1fGIKKniGiseBQ1PuXjr7CaEpJw4Y3yNVRGoXMTzrZfScyTKWRGjsEmfRNhvzQjeH0b7M6uA4Mx4XGz/ELrY8OlT9qQkPIsF//XCuW5POr1+43AiO9xWBSNUFixt7yqroD3VAWNk1X4LVBgKIAzw3QcCynlwiwduqum7/cKpUjLIWeZemAj47dsxr95Nutn1Gesf3++GdGS86fsTJ6rppECZAkJCaD6JBZKMyUW5nI/+SArb2SQdVIGWULiocU5z59B++YzY0UafQ7M5KJ9LAu6d2fawHD2hCymVF50x+M1BGJLNywIB4w6ZT2X0XEROTaIiBgoIp3XqcsEZFjcnj2uhFIrb843/4ToIemkPTIH1fV0Arb2JeLnYJxPL0CmvX5bRtlgqyZ3TCMS458h7fsu6O1UuL+xk2C/ZbhM3o/iYsW6a7mFQN0RchpEKwlZp0DjL5D6rp4jfqWcfVNH8Vkz3IsECH3sEqPXbWdG9C+0fiaJgz/6MqlRL2Y90YFTW90q6qhdq0gBsoSEBFDNLhY1KLGoega5Bor0JJs3CYn/DJYlDnQ5OZ7pP5zl2e3fodRr+L7ti0x4ypsNTd4jT1Oxrrci6tAYHcZmIAXsJo0RKHGnLu8Cd84eV4RBZUNW5GhiBiWR3OEndBon6u0bSdQPnngcegfl9QvAP+QXChl5A4NI2TuQlB39KGztjvPHRwgKWIbH83+iOZld4bkEmYBDDzkRW1TUP6TEsaeMSwv1HAstJX6Qlrz95lXguQXnMfzzA8xOWU3fqcdJO+nAp907M7nxE+z+NgDtPSZtqooUIEtISADVrEE2w8XCXAyy+yiDXGbzJmWQJST+MygMKpqfGcqENccYvWEbfpkt+K3xNCY85c13j75Ihl3sXeew5ykEZETjxgXeRkCJH6sBTM4eV4hMwRW/AcT3OkBcz33keXSgbvQnRK7yxXfH01jknigfWi6/EAQKW7mTtroHZ2Kf4cqLEdisTSag6Sp8uv2C1aZzleuUG8gIXKak0RkVHmPlXNth4FRbLdFtSslZo0fUmf6zWDmW0HNCNJ+eWcPzi/cA8M2LrRgX2I/1H0WSn6Ou8mWpCg92mxMJCYlqozo66YExQNbWYEJVVFStk56sBjrpSRlkCYn/LgICIRntCclozyW7eLZFzuVA0LfsDV1MeFpXOkSPJfRCxwqzwXIs8Wc9xSQAcjQEAH+3rq4Orru2IMV1Naq8FFxPz8cp4Rsck74nz60dmZFjuebd/RaNsua5byn1t+Xi3LZkvtcch8Wncfz8JD69NlAc6kDuqAZcHRyMaHF76Kj2EKg3Q4HnBDlZyw1kzNeROFiH2gfcXpfj+qwcubVpP5dSbaDNM8m0fjqZ2O1ubJoTztr3GrHhoyhaPZ1MlzdicQuuuK12dSJlkCUkJIDq9EGmZjPIVXaxqLlOelKjEAmJ/zZ1r4bw1O5FfLQinZ6HPiDd6TjzH+/Mh/0bsC94aaVONxqCy4NjMF9akcFULrMCkYoL7ABKbfxIbzGX6MHppDf7GE3eGQK3PEH4z2E4xX2JTFcI3Cq/MNhryHmrMYmJw0hf1hlRLcfj5e0EByzDZdpB5FmFFZ5LbiXg9qqcRqdVBP+sQOUhcG6cniO+pZx7R0dJunk65fAOFxm3cSvTT/xCiyEp7Pk2gHcj+zCnd3vi/qpbozplKUCWkKiArKydHDnyInv39uHIkRfJytr5by+pxilrNX3vLhbmtZoGELV6tBfyyN+awtXVsVxbF0edtHgU13JuH1uuQa6CxELQ3uIveq8ICCj0KrRyKYMsISEBVsVOdD8+iekrUnn6r28QMbD8seeYOMSHTQ1nUKDOrbZzGSjlKms5JwzlFH5k8gk6rlY6Xq+2I7P+W8Q8mUJKu+8xKK3w2fMykT94435kCorCS+VjyzLLokrOtSHBJB8cxNnNvSls6orLh4cI9l+G+8vbUMdervBcglzAsZecyB0qIvcqsesiI2OenqNBpSQ+raXgmHn7sEfYNZ5btJ9ZyavpPfkEKYed+F/nLkxt/jj7fvBFp62erPstP4M5hs/3O40bB4gHDsz6t5ch8YCTlbWT5OQvMNzUiEImU+Pv/youLm3/xZXVPHXqPMHYsUl8+GFcledY+Woe0RtK+Cjd2aTxuitFXHj9d/I2JiKzUCJ3sEAs0lJ0WaTQK5j0AWMp8gouHy8rzafRtzakN/+EzKhxJq/rEh+RIUyggVhU3vWqOhg93JaWic8ycN/captTQkLi4UBEJM5jK1vrf0qs1xaUWgtaJA6nQ8xoXK8FVcP8BvLYRCazKBB2IBMtceR5XBiFGr+7HCxidWk3rjGzsEvdgChTkhswlMzIMRQ7RNwyVPPct+Vfq+Iv4/TZSey+i0NWrCe/izc5oxtyvb2XMe1bCcWpIhc/15P1jR59Pti0FnAbJcfhcRmC3LwAt7RIzr4f/NgyL4yMeDvsPa7T4ZV42r2YiKV9xW21yxiuGn5UFMUmdzuHlEGWkPgHaWnf3xIcAxgMJaSlff8vraj2UKsNlJbeqwbZPInFhZc3IshlBJ9+jfBL4wiJfY3Qs6M5+fEWCvzr4/PdBwjavze8e8kgAzVi9SYV6UlISFSEgEDYhU688ftmJv8UQ9PkwewL+Yb3ngzmiy69SHD7656K8gRk2NKDILYTIh7Hjj5k8wWnCSSFARSwr/L5BYECt0dJ7vwrpwYmkBPyIg4pq4hYE0ng712wSd9MmYbhZq1yaYgDGZ+3IyHlWTKnPoLmRA6+3X7Fv8lK7JbHIZToKzydpp6A78cKGp9V4fOJnJJ0kYQBOo5Harm4UI/+uunXQWWh57Hnz/DhiV8Z8+tW3EOusXpSY8b69ee70c3ISjatM+udkAJkCYl/UFJy+2P9O73+MKFWG+5ZYqE0s5Ne/vazuH/aGZWnzS2vi0oVGb1eRXPpHLLSvyUMokxpLGOpQpEeUP3d9PRqSYMsISFxVzyuRPDMzm+YsSKN7kcnk+y6lzk92zGjb2MOBfyAXla5jtgU6tAAH74jgnO48jb5bCVRaEUiLbnCakR0lR5bYhtIWqsFRA9O43yT6Vhcjiboj66Er4nEMWEJgq74Nj9lvZMF2ROakpg0nPNfd0AwgOcLWwkK+hbnmYeR51bsD62wEXAfpaBRnIqgFQoUDnB2lI6jfqWkTtRRmvH/9u47PMoqe+D498xMMhNSKGlAIBB6CQEFQVBEROwKdhCV36qsyqqr6K6Lrq5l7X1Zdq0IriDWxbYiNpCiICgQQq8JAdIgpNe5vz9mEtKZJJNJCOfzPHlw7rzvfe/7PjE5uXPuuZ7//rBYYPCFyfzpq294dM1nDLt8H0vf6MP9Aycy6+qz2bEqvMF5yhogK1WF3R5Wr/bWxOEo9UoVi5JC8DR9yy8qhOzv9+DMK8YUl2KKS3HmF2PNzaL92iUUdOxe+WM7EYzVXu8qFuJOqzBeVHsoTgAAIABJREFUr2Th0BxkpZTHQvIjuWztYzw1P4kpy16n2JbPnHFTeHByDEsGP0eef+15xJ7wJ4ooniKW/XQ1/6SENPbI1STQi1ReppTsWs8tdYRy6JQHiJ+8lz1j5mLESsyPNxO3sDudfn0cW4FroqhisGzsVjKnDmDnr5PZ++UECuJCiXz4Z/r2mEunO5fiv/1IjdcSmxB2tZW4Ff7ELvMjZIyF5BdKWde7iB03FZO7vn55yt2GHGHanJW8sPNjLv7TJrYuj+SJsy/i8TMv4uf3u1NaUr80Ds1BVqqKkzkHuW/fczn99MPMm/drg/tY/GQOXzySy8s5Edj8j/8DKWfpXpJ+twhHXCQBp3TCEuiHM7uILd8FErx9HYmT7ifzlLGVzhkyrx0ZvW8kadQ/PB5XBu+yT25ggNmGg8bn/pV57OpYIo724bYln3itT6XUycOJk4Tor/g27gW2Rf2AvTiQUVtv4pz4uwnPPk4esQcMpRzlc1J4gVxZgcWEEMY0Ivgj/nQ9zsmG4APf0TH+RdomfYXT6iCj942uPOV2/coPq5ijDGBPyCDslfW0XbAVKXaSfVEMGXcPIfesqLrzlHcZDvyzlNS5pThzoe1YofPdVtqdb0Es9QtwC3NtLH+nJ9/MGkDKzhBCu+Uw/g9bWPjn4R7lIPs0QBaRDsBbwHlAOjDTGLOghuMeAR6ESp+FxhljdtfVvwbIyltSU5eRmPguhYXp2O1hREdfXy049uSYE01c3DkMGJDFwoVrG9zHty/ksmhmDs9nhOMI9mw2uiQ1l8z3N5H360GcWYVYgu0k5JxJ+shLKW4fUe34we9GktltIvtGv+bxuI7wIXvkGvqbjQQwyOPzjufJK4YSkteROxZ/6bU+lVInp8TQ3/gu7iXW9lyIU0oZvG8C4zfcR8+UUV7pP5c1pPISR/gQgPZcRQT3Echx40UcRzYTGf8SoTv/g6W0kMyuF5MyaAbZncdWCnorBsvWlDxCX91Ih9fisaUXkH9qBOl/HMLRq3qBX+3pfCWZhpQ3Szk4u5SiZAjo61rQFz7FgjWgnrsMOmH9F11Z/PJAtq+IBKRFBsjv4UrruBkYAnwJjDLGJFQ57hGglzHm+vr0rwGy8pXWOss8fPgYOncuYNGi1Q3uY+nsPD66J5unD4QTFHb8ADnnx320GdoJS6B/pfY5cybUes6g97qR3Wkse8+e6/G4Mvmc3XIZfc0aAjnN4/OO59kJZ+BfEsDdX37rtT6VUie3I22SWRY7m+X9XyPXcZiYlBGM2ziDU/ZcgdU0fo+3QvaRxj9J53WckkWQGU0E99CWyxDqXodiy08lYvO/CN/8L/wK0sgLHcKhQTM40uNajLXyz/GyYFnyS2g3fyuhr6zHse0IxVGBZPxhMIdvicXZrvYd8pzFhowPnRx4pZTc3wy2MOh4q5WOt1nxj6x/abc960J5dOSlLauKhYgEAlcCDxljcowxK4DPgBt8NQalvKW1VrrwVhULgGIPF+rtn/YZhbtcOWqm1IkxxpW/XMcf78ZiR5z1WxhnKc9B9vZ207pITynlXe3zopi45kmenJ/ItStmkePI4M3x1/LQ5F58O+gl8v0at5OcnW504TkGkUSUeZEiEtktV7CZfqQxm1Jyaz23JCCCA0MfYePkRPaOfgMpLaLH0hsZtDCGjuufxlpwrDZyeT3lABtHboll54Yp7F10CYV92tPxgVX0jXmbjjN+xG/30RqvZfETwq+zEvezHwO/8SN4hIX9T5SyrmcRO28tJi+hfnnKMUM9r0Pty0V6fYASY8z2Cm0bgIG1HH+piBwWkQQRub22TkXk9yKyVkTWpqc3/daDSkHrrXThqmLRyJ307K6/6j0t9dZv250ExEUCIFYLIoKI1Jmn5rQ5GlzmzftVLHSRnlKqadhLAhmbcAePvr+V2xYvokNONB+NmsHMKV356PR7yQja16j+rYQQyT0MZCcx5gOshJIkd7CJriTzAEUk13qusTlI73cLCVdtYvsFX1HQfgBdfplJ3Htd6bryTuxHdwJUqnyBRci5KIa9X1/OzjWTyJrYg9BX4+kz4D90veZ/BPx0sMZriQhtx1jo/18/TtnkR8TvLKQvdLL+lGI2X1xE5rdOjxeGe8qXAXIQUDWCPQrUVKzuA6A/EA5MAx4Wkck1dWqMed0YM8wYMywsLKSmQ5TyutZa6cLhKKWwsPE76QGU1DMOzVt3gILNaTgLay9FVMZY6l/FwlJeB9nbVSx0Blkp1bQsxsqQfRO477Mf+csna4hNupDvB73CQ5N78ua4yewJX9Oo/gUb7bmafvxMH7OSYM4hhWdIIIa9TCWP9XWcLGR1vYDtF31DwhUbONLjGsK3vkbsB33oueRygg4uB2MqB8pAwZBwkt8+j207ppJ+76kELttPzzEf0ePMDwj5cAeU1Dw7HNDHQs9Zfgzd5U/0o1Zy4w2bLypmw6nFpMwrxVmPOvx18WWAnANUjWBDoHq9EWPMZmPMAWNMqTFmFfAKcJUPxqiUR6Kjr8diqZw3ZbHYiY6uV9p8i+Pv76Sw0DspFp7OIJf91b//ti/YMeIN0p5dSeGOuj8Gc1rtSL1nkF0pFt6eQdYUC6WUL3VPO41bvlvI3xfsYVz8PWyK/pJnrhjB85eNZn33RTil5o06PBXEKHrwEQPZQRi3k8nHbJVT2M45HOVLDLWnNeSHxrF3zNvET97HoSEzCT70I/2+OIv+n46g/a6F4CypVk+5JCqIlCdGsW337zjwyhishwuInrKYPv3fIfSV37Bk1bwznl+Y0GWmjaE7/On1pg0Edk0rYV2vIpKeLKE4o3GBsi8D5O2ATUR6V2gbDCTUcnxFBvD+RtvqhJGauoy1a6excuXlrF07jdTUZQ3uKz7+YVaunFj+FR//cL2vFxExhvDwsRz7X8hCePjYBi/Q8+b9NYbD4YUUC4frf9ViDwNkcadSiL+V7v+dhCXETtLvPiV01WfYjtacstKQOshNOYOsKRZKKV/rkNuVK39+jqfe3c/Vq17icFASr55/OX+7ti9LB86mwJbTqP7t9KArrxDLfqLMsxSynV1yCZsZ6FrcR80bgQAUt+lE8mlPsPG6JPad8W+sRUfp+f1kBr3fk8iNL2AtcuUcVwyUTaAfh2+PY0f89ez78CKKuwbT6U8r6NvjbTrevwK/xJrrN1vsQsSNVgav82PA//wIPMVC0iOlrOtRxK4/FJO/rX55yuX9NuisBjDG5AKfAI+JSKCInAFMAP5T9VgRmSAi7cVlOHAX8KmvxqpalrKKEYWFaYChsDCNXbv+1aAgMj7+YbKyNlZqy8raWClI9uR6qanLSEv7Acr/knaSlvZDg8bkzftrLLvd6b0Ui3rGjGIRnHnFhP/xdLq9fxVt41fQ7b1nCN76C1JaOe3CaXXUeyc9aaJFejanziArpZpPQHEI4+Lv5vH3djLtmw8IKghj4Zl38MD1Xfnv8JlktjnQqP5ttCOSPxHLHrqb+VhoQ6LcyiaiOcDfKCal1nOdtjakDbiNTVdvYcd5n1EY3IOuq+8jbkEXuv50D/7Ze4EqecpWC9kTerLn+yvZteoasi/oRug/1tOn7zy6TFlMwNqarycitDvXwoDP/Bjymx9hkyykvuPkt0HFbJlYzNGl9ctT9vVOetOBACAVeA+43RiTICKjRaTinzqTgJ240i/eAZ4xxsyr1ps6KXizYkTV4Limdk+u580xtaSKGK4c5EamWLjiUI9TLPJ+O0j21zspzS4ib1USWV9sJ/u7PWSMvBSnnz99XplO8NbK+XXGWv9FepbyFAvvzvb6lTg0QFZKNTursTF099Xcv+hn/rxoFX2Tx7Fk8LM8cF033h57A0mhdeQRe0DwowPX0Y+19DZLCWQUh3icTUSzj5vJryshQCwc7XYp2y/5gc0T15IZfRnhCf9k0Ps96fHtNQSmukqLVk2/yB8Wyf53L2D7tqlk3DWE4K/30XPUB8Sc8zHBn+6C0ppnh9sMtNDrNVeecpe/Wsn+xUnCecVsPN3z7bwbX0yvHowxh4GJNbQvx7WIr+x1jQvy1MnJ1xUjPLmeN8fUkipiOByNz0GubxWLw2/+ytGPt2AKSzgyfyPZX+/EGIjKTKC0TQh5XftRGhBU6ZyG5SCXpVg0QRULiwbISqmWo0fKSG795iPSQnbxQ+wsVvZ9i9V93qVv8ljO3XgvAxMvxNLAOVJBCGYMwYyhgO2k8jIZzCVD5hBizieCGQQzHqklMzYvfCh7zpnP/uHPEJEwi/Ctr9Nhz4fkRI7i0KAZZHabCBYrBXOmltdRLo4O5tAzZ5L61+G0f3szobPW0+3q/1HYsy0Zdw7myNQBmEC/atfyjxCiH7YR9Scr6QucHHjZ8/xsnwbISjWE3R7mTj+o3t5c1/PmmHx9f3WPpbTROchlKRbFHk7Udpl9MV1mX8zeaz6k/eRY2l7eH6h7oxBjddQ7QLY05SI9WwEGU+svBKWUag7hWT25ZtXLXLL2EZb3f52lsbOYfeElRB7py7j4uzl9+1T8SwMa3L+DPkTzLzrzOGnmVdL4JzvlfBwmlgjuoQNTytd/VFUc1IXkEc9w8NSHCNs2h8hNL9Pr26soDI4hJfZu0vveVKnqheOmeTiD/cm4awgZ0+MIWbSLsJd/o/PdPxLx6GqO3BJLxvQ4SqKCql3LGiBE3mwl4ncW3L8KjsvXKRZK1Zs3K0aEhMQdt92T63lzTC2pIoarikVjc5Bd/3o6g1ymy2uXEHxh7+MfiGsGub6L9KQJF+kZMTgtxy9Pp5RSzaFNUTvO3/Bn/v7ebm7+dgH2kiAWnHU7D0yJ5rNhD3E04FCj+rcRSiceJJa9dDNzESwkys1sojsHeZwSav9E1OkXRGrsXcRfs4Od535McZtORP/0R+IWdCFq9f345ewHqqRf2CxkXdWb3SuuYdeyq8g9uwthL/xK397ziPrdEhzrq086gWuti6c0QFYtXkTEGHr2nI7dHg4Idnt4g7d0HjTosWpBckhIHIMGPVav63lzTN7sq7HsdidOp1BS0vCZ0PJFekWeBcgFCank/LAHsVmwOGwYp6EkPQ97yj4C9u+gzb7NWHMr77JkGpRiYQFj8/5GIU5X4K1pFkqpls7q9OO0XZOZ+ckvzPhsKT1SRvHVqU/w4JRuvDPmZpLbb2pU/xbshDKVfqynl1lCG07hoDxMPF1J5DYK2FrHyVYyY65g62Ur2XLZT2R1OZ+O8c8zaGEMMT9cT5u0deWHVpxZzh/ZiaT3L2L7lhvIuH0QIZ/uptfwhXQ//78E/W8POBtW7k1TLNQJIStrC4WFGbiqPGSQlbWlWgBZtUJF1cC3TGTkOAoLD1JYmI7dHkZk5Lhqx0REjPFpgOrr69XGbncteCgstGCzNayWZlmZN083Cjk8dz2m1BA0NgYAZ14xiTf+l9jvXqS4XQR+makkT/gDhy74v/JznBY7lnpuNQ2uNAvv5yC7AuQSayGUVP9oTymlWhpB6HNwDH0OjiElZAffxb3ET33msqrfHAYknc+4jfcwYP95DU4bE4QQxhPCePLNFlJ5gQzmki6vEWIuIZIZBHF2rf3nRp7O7sj38c/eS8SmfxC+7U1Cd84nu9MYDg2awdHoS6qlXxTHtOXQC2eR+tAIOryVQOjsDXSf+AUFfduT8cchZF7XF9Omep5ybXQGWbV4O3e+SkrKYiqWVEtJWczOna+WH+NJ+TbwXkm1llSazZvKAuTG5CGXpVgUF3j2V3tpZgHWIH8AnPnFWIP8cfQP4+AFv2PjU1+SMeIipKRyoXhTttV0PbcWFexer2JRFiBrLWSl1IkoMqs31634F0/NT+KyNX9nf4cNzLr4Ah6/Ko7DgUmN7j+A/nTjTWJJpKN5mDxWs0POYStDyeBdnNS8EQhAUXB39o98kY3XJZE04nn8s/fQe8kEYj/oR/jmf2MpyQMql4lztrOTfu+pbNt2I0lzz8O0sRE1/Qf69pxLxCM/ezxuDZBVi5eSsuS47Z6UbwPvlVRrSaXZvMnhcM0aNyYP+VgdZM+CV2s7B858V+kdS4Drr/vSo4Xg3kDEWKxYC/IqneN052zXf6Ge3es5yH6lrhUfWupNKXUiCyoM5aLfHuSJBXuZ+sNcwrJjaJfXuVF9FlnzOdhuC8kd4vEjgs48SiyJRJs3MBSwT24ggRgO8TQlHKm1n1L/tqTE3Uv8tbvYdc57lNrb0W3ldOIWdKXzL3/FL+8gUKWesp+Vo9f1ZdfP17L72yvIG9mJ8Kd+8XjsmmKhTgC17YJT/91xvFVSrSWVZvOmiikWDWX1c8W2nqZYBI7sSvqra8n8MIF2Vw/k8Lz1FCUeJXdALAClbYKrnWOsrqDU4iyk1NMlybg2C/F+FQsNkJVSrYef087I7VMZuX3q8Q+uw+GgROaPvo0CvyxS2+4gOn0o0759H0dxMGHcQig3kWW+JpUXOSAzOWQeJ5SbiOBu7PSsuVOLjSM9J3Gkx7UEpawkMv5FOq1/ko4bn+Vwz+tIGTSD/NC4aukXeWdFkXhWFP7bj0Dsupr7rnqpRt29Uj5R27dp/b99ayudVt+Sat7qp6XxRoAsItgcnlexaHtFf0Iu7MX+6V+yqf3THJz5HW0v78fRuNEAHB04iqz+wyud47Q2Zga5CXOQlVJKUWDL4d/nTSSgKIQpy1/juf+kYHX6sbHb5+XHCBbaciG9+YZ+Zj3tuJp0XiOB3uziCnJYgaGW3yMi5HQ8k13jP2HTNdtJ63cr7fd8yMBPBtPnf+MJSVpcnoJXcVa5qE97j+9BA2TV4kVGnnfcdk/Kt4H3Sqq1pNJs3uSNABlcaRaeVrEACL9nJAP2z6DP+tsYeOBewm4/rfy97P4jyBo4qtLxZTPI9a9k0cSL9JRS6iRnMCyNnUW+PZNbvltI5yMDAbCV+rOjU83rdNowmO7MJZZ9RDKTHJaxXUazjREc5n0MtZfRLGzbi6QzZrFxchL7T3sKx5HN9Fl8IQM/GkjY1jeREldaXaX0Cw9oioVqkNTUZSQmvlteCSI6+voGV2FwLcJbgitlwkJk5Hn06nVb+fu9et1GaupyjMktbxMJrHTMoEGPsXJltU0aq1WxiIgYw44dsyu1OZ2m2thXr76JkpLD5a9ttg6MGDGnUj9ZWVsqjTs8fGyDn4E3n2dj2O2Nz0EGV4Ds6UYhFVnbOihOzsJZWIp/ejJO/wBKgtqBpXLAXjaDXN9ayBZdpKeUUk0qOyCVpQNnc+XPz5W35doPE1DUjsjMvpWOrbrBkh+diOIJOvIAh807pPISe2USB0w04dxFGNOwElLjdUsdHTg05C+kDJpB+93v0zH+Rbovn0bULw+QNmA6qQOmUxIQ4fF96AyyqjdvVnDwpELFunV3VgqOAYzJZd26O8tfr1x5ZY39V21ftWoKVFsxW+Rud6kaHAOUlBxm9eqbyl+npi4jLe2HSuNOS/uhQc+gJVXE8NYMsl89UiwACramk3znV+wY8QZbB/6L7ae+Rt8XbyVm3iO0//XbatUqTANTLERTLJRSqkmt6vs29uIgTts1ubwtKew3MgP3E5LfEQCn+3enIJRYitgXtpYi27HF2FYCCed2BrCVHmYR/sSQLPcRTxf2cy+F7K31+sbqz+HeN7D58l/ZdvH35EaMoPOvjxL3XjTdfpzm8X3oDLKqt7oqONR31rOuChVlM8QFBTWXmancXlvN3srtVQPtmtqrBsc1tXvzGXizr8byWoqFv3hc5q0gIZXku77CFh5I9H+uwK9LCOJvpfRwPt/PdNLp67lYC/JIP/PYJwTHZpDrv910CZn1Oud4/DRAVkqpcofabSFu32XlrzOC9pHQdTEWY2PYzkkAOC0lWJz+rOm1gDW95lPgn0VqyE7Gxd/N+RvuLz9XsNCOCbRjAnlmHSm8SCr/IJVXaMcVRDKDQE6veSAiZHceS3bnsdgztxEZ/xJhO+Z5fB86g6zqzbsVHLxXocKXvPkMWlJFDG/UQQZ3DrKHGQd5vxwAq4VuC6+izfAo/DoHYwtrg71PKAcvvoW00VfQft03lc4pr2LRgO2mvb7VtFNTLJRSqkyvQ6NJD9kFgFNKWdnvLQ60T+DsTXdgwUKppRib058Cv2wWnnEH/ZLP5ffffMR9ny1nXc8P2dFxeY39tmEoMcwnlt1EMINslrBNRrKNMzjCJ5haJ8qgsF1fEke/ysbrPK/rrAGyqjfvVnDwXoUKX/LmM2hJFTH8/b2YYuHhIj1LgA1TWIIxBlNhS1BjDJbCfPzTD1ASVHnl8bEqFvUPkJsqB1lnkJVSCnqkjORAh008ecVQXrn4PBK6fsWorTcxcP/5AFicruSFZQP+TdThOM6Nv4eQ/EgisnohxkJq2x2AK7iuiT9d6cKzxLKfLuYVijnAHrmSBPqQyixKyal1bCUOz3+vtuwoRLVI3qzg4EmFCoeja43HVG6vbVFZ5XaRwBqPqthus3Wo8ZiK7d58Bi2pIoY3NgoBsDnE4xzkNiO7YosIZPe575D5QQLZ3+4me8kuMhfE023BkwTvXE/q2GsqnXNsBrn+KRbezkEur4Ns0QBZKaU6HxnIo+9vY/SWWxkbfxfTF3/O0D1Xlb9ftiivQ040/iVtytvTQnbRNq8T+f6uNDiLsZLjSCehy9c1BstWgojgLgaykxjzEX5Esl/uYhNdSOZ+itjfqPvQAFnVW0TEGHr2nI7dHg4Idns4PXtOr5Yvm5q6jLVrp7Fy5eWsXTutxkVnvXrdRmTkBRz7VrQQGXlBpQoVQ4fOqhYkOxxdGTp0VvnrM874GKrt6S7u9mNGjZpf4z1VbB8xYk61ILmmKhaePANPeLOvxnI4XDPIRUWNT7HwtIqFf3Rbur5xGUHnxJD2/CoSr/+ExOs/IfXpFZQ6gth748Pk9oirtFCvoXWQm3KRXrHOICulVLnRW37PkH0TaJvfkSWDn+O72Fcqvd/pSH+OBCWybMC/SQz9jY9Ov4/tnZbSP3k8AB+P+DOzLryQRcNnct/UMNb0WlDjdQQr7bmSvqyij1lFMONJ4Xk2EcMerieP3xo0fl2kpxokImJMnQFcWWWGssVnZZUZys6tqFev2yoFxDWpGAzXdj2Lxb/SYjeLxZ/U1GWVrlex8kVF69bdWekaFYPh2hzvGdSHN/tqDO/lIEPeYc+rWFjbOYh88CwiHzyrUvvKORNc/2FM+dbTAKZsq2ln/WeQvb2TnqZYKKVU3XofGFOel5zvfxSnlNLl8GCuW/4qnw/7G4lhv7Kx+6ecvekOog4PYnm/N/hxwL+5fcki+iWPY12PD1nTaz5D9k6sNOtcVRAjCeJDCtlDGv8gnTc5IvMJMmOI4F7acrHHY9YZZNUk6qrM0JzX86wixsnrWB1k31WxqMgYU56LbJzm2KyxVP50wNnAFAst86aUUr4Xkza8vOxbcod4Phh1NykhO+h16EymLn2btnmd6HRkABN+eYKk0PWs7vMfLln3CP2SxwEQnTaUzV2WkO1I8+h6dmLowkvEkkSUeZ5CdrNbLmMz/T0eswbIqkn4ujJDS6oEcSI7VuatcTnIfg6hpGq5aQ+IiOvL4vqqGhiXMS1wkZ5WsVBKqePrdehMAgtCefKqU3jj3Gt5bsIZZAYmM3H10ziKg1nbcyF+JQ7Gb7y3/JztnZfS+9BoggvCcUopGUH7WNX3bb6P/Ued17LRjkjuJZZddDcLat1kpOZzlWoCdnuYe+OL6u2t4Xqtlfe2mq7fRiH11fA6yHaQUowpRWpd2Fk/FixYS/10BlkppTx0zU8vce7GGWzvvJRx8XfTI2Uk4Kpc8VOfeVy78ljKY5YjlcTwdUQc7YN/SRuW93+dn/rMxV4cRJEtjx9iZ3H714vKt7SuieBHBybTnkl4OjesM8iqSfi6MoOn1/OsIsbJy2IBm83ppTrITRcgmwZuNS24zvP2LLJfqUNnkJVSqh465Hbl9B03lAfHALsjfsZqbMQmXVi+296G7p9yOGgfQ3ddw56I1fzY/1WG77iePyz+gj99toJORwawN2KNR9eUaov5a6cBsmoSvq7M4On1PKmIcbJzOJxeqWJR0oQTqmU5yPWtYmHBdV5T5CGXaICslFKN0iVjMJGZfdkfugELFjZ2+5z1MZ/QLe00eh8azScj/kz/5PEM3X01Nqc/pVJC+9wuHGi/qTyg9hafpliISAfgLeA8IB2YaYypVrdDRAR4GrjF3fQm8BdjTNNNSSmv83VlBk+vp8Fw3RyOUgoKGpmD3IAUi8wPE7B2CCB4XI/jH2yxYcTagBnkpgmQ/UodmmKhlFKNYDA4SoLokTKSly8+l8H7LmNT1684b8OfGRd/N7/GfEyxtYDhO6YQXBAOgNXY2B25imE7J2HBgsHUa5a4Lr7OQZ4NFAGRwBDgSxHZYIxJqHLc74GJwGDAAN8Ae4BXfThWpU5KdrvTCznIrkV6xhikloV2VaU8/iOOAeGeBci48pDrP4PcNCkWNk2xUEqpRikLbC9b+zjDdk0iMWwd4zfcR7f0YThxkhi+jt6HziI0u3v5OetiPiI1ZCdjN91VqQ9v8FmALK6tyq4EYo0xOcAKEfkMuAH4S5XDpwIvGGP2u899AZiGBshKNbnBg48SFZXfqD7aR1uJHmrDWQJWP8/OcQyKwK+L5yuM88KGUdymU73GZSOSNmYo3s4u65IxmA450V7tUymlTladjwystOjOgoVc+2GKbLkEFIdgMBRbC3j/zDu48LcH8C8N8OrsMYD4KmtBRE4BVhpj2lRouw8YY4y5tMqxR4HzjDGr3a+HAT8YY4Jr6Pf3uGacAWKBTU10C6pmYbjSZZTv6DP3PX3mvqfP3Pf0mfuePnPf61tTPFmVL1MsgoCsKm1HgZoGGeR+r+JxQSIiVfOQjTGvA68DiMhaY8ww7w1ZHY8+c9/TZ+57+sx9T5+57+kz9z195r4nImvZyJTyAAAJKklEQVQ9Oc6XVSxyoFqF5hAg24NjQ4AcXaSnlFJKKaWami8D5O2ATUR6V2gbDFRdoIe7bbAHxymllFJKKeVVPguQjTG5wCfAYyISKCJnABOA/9Rw+DvADBGJEpHOwL3AXA8u87q3xqs8ps/c9/SZ+54+c9/TZ+57+sx9T5+573n0zH22SA/K6yDPAcYDGbhqGy8QkdHAV8aYIPdxAjxD5TrI92uKhVJKKaWUamo+DZCVUkoppZRq6XSraaWUUkoppSrQAFkppZRSSqkKWkWALCIdROS/IpIrIvtE5LrmHlNrJyJ3iMhaESkUkbnNPZ7WTkTsIvKW+/s7W0TWi8iFzT2u1k5E3hWRgyKSJSLbReSW45+lvEFEeotIgYi829xjae1EZKn7Wee4v7Y195hOBiIySUS2uGOXXe71WKoJVPjeLvsqFZFZdZ3jy41CmtJsoAiIBIYAX4rIBmOMloZrOgeAvwPnAwHNPJaTgQ1IAsYAicBFwAciMsgYs7c5B9bKPQXcbIwpFJF+wFIR+c0Ys665B3YSmA380tyDOIncYYx5s7kHcbIQkfG4ihFcC6wBOjXviFq3siIQACISBBwCPqzrnBN+BllEAoErgYeMMTnGmBXAZ8ANzTuy1s0Y84kxZhGuaiSqiRljco0xjxhj9hpjnMaYL4A9wNDmHltrZoxJMMYUlr10f/VsxiGdFERkEpAJfNfcY1GqiTwKPGaM+dn9Mz3ZGJPc3IM6SVwJpALL6zrohA+QgT5AiTFme4W2DcDAZhqPUk1ORCJxfe/rpyRNTET+JSJ5wFbgIPC/Zh5SqyYiIcBjwIzmHstJ5ikRSReRlSJydnMPpjUTESswDAgXkZ0isl9E/iki+mmsb0wF3jle6eDWECAHAVlV2o4Cwc0wFqWanIj4AfOBecaYrc09ntbOGDMd18+T0bg2Oyqs+wzVSI8Dbxlj9jf3QE4i9wM9gChcmyh8LiL6SUnTiQT8gKtw/VwZApwC/LU5B3UyEJFuuFIV5x3v2NYQIOcAIVXaQoDsZhiLUk1KRCy4dp8sAu5o5uGcNIwxpe70rS7A7c09ntZKRIYA5wIvNfdYTibGmNXGmGxjTKExZh6wEtc6B9U08t3/zjLGHDTGpAMvos/cF24AVhhj9hzvwNawSG87YBOR3saYHe62wehHz6qVce8w+Rau2YeLjDHFzTykk5ENzUFuSmcD3YFE17c7QYBVRAYYY05txnGdbAwgzT2I1soYc0RE9uN6zuXNzTWek8yNwNOeHHjCzyAbY3Jxfez5mIgEisgZwARcs2yqiYiITUQcgBXXLzCHiLSGP7hasn8D/YFLjTH5xztYNY6IRLjLMAWJiFVEzgcmowvHmtLruP4AGeL+ehX4Ele1HNUERKSdiJxf9jNcRKYAZwGLm3tsrdzbwJ3unzPtgXuAL5p5TK2aiIzClUZUZ/WKMq0loJkOzMG1KjEDuF1LvDW5vwJ/q/D6elyrch9pltG0cu68qVtx5b8ecs+uAdxqjJnfbANr3QyudIpXcU0m7APuNsZ81qyjasWMMXlAXtlrEckBCowxac03qlbPD1fJzn5AKa7FqBOrLHxX3vc4EIbrU/AC4APgiWYdUes3FfjEGONRCq4cZxGfUkoppZRSJ5UTPsVCKaWUUkopb9IAWSmllFJKqQo0QFZKKaWUUqoCDZCVUkoppZSqQANkpZRSSimlKtAAWSmllFJKqQo0QFZKqROMiPyfu0ZwXcfsFZH7fDWmuohIdxExIjKsuceilFKe0ABZKaUaQETmuoM+IyLFIrJbRJ4XkcB69tGqds9qjfeklDr5tJad9JRSqjl8C9yAazey0cCbQCCuHfiUUkqdoHQGWSmlGq7QGHPIGJNkjFkAzAcmlr0pIgNE5EsRyRaRVBF5T0Q6ut97BNfWpxdXmIk+2/3e0yKyTUTy3akSz4qIozEDFZG2IvK6exzZIrKsYspDWdqGiIwTkU0ikisiP4hITJV+ZopIivvYd0TkbyKy93j35NZNRL4RkTwR2Swi4xtzT0op1VQ0QFZKKe/JxzWbjIh0An4ENgHDgXOBIOBTEbEAzwMf4JqF7uT+WuXuJxe4CegPTAcmAQ82dFAiIsCXQBRwCXCKe2zfu8dZxg7MdF97JNAOeLVCP5OAv7nHciqwBZhR4fy67gngCeAfwGDgF2ChiAQ19L6UUqqpaIqFUkp5gYgMB64DvnM33Q5sMMbcX+GYG4HDwDBjzBoRycc9C12xL2PM4xVe7hWRJ4H7gIcaOLyxwBAg3BiT7257SEQuxZUi8qy7zQb8wRizzT3e54E5IiLGGAP8EZhrjHnTffxTIjIW6OMed05N9+SKzwF4yRjzubvtAeBG97hWNPC+lFKqSWiArJRSDXeBu5qEDdfM8afAne73hgJn1VJtoiewprZOReQq4G6gF65ZZ6v7q6GGAm2AtArBKoDDPZYyhWXBsdsBwB9ojyuw7we8UaXv1bgDZA9srNI3QISH5yqllM9ogKyUUg33I/B7oBg4YIwprvCeBVdaQ02l1lJq61BETgcWAo8C9wCZwGW40hcayuK+5uga3suq8N8lVd4zFc73hvLnY4wx7mBdU/2UUi2OBshKKdVwecaYnbW89ytwDbCvSuBcURHVZ4bPAJIrplmISLdGjvNXIBJwGmN2N6KfrcBpwJwKbcOrHFPTPSml1AlF/3JXSqmmMRtoC7wvIiNEpIeInOuuJBHsPmYvECsifUUkTET8gO1AlIhMcZ9zOzC5kWP5FliJa4HghSISIyIjReRREalpVrk2rwD/JyI3iUhvEfkzMIJjM8213ZNSSp1QNEBWSqkmYIw5gGs22AksBhJwBc2F7i9w5fNuAdYCacAZ7kVszwEv48rZHQ883MixGOAi4Hv3NbfhqjbRl2O5wJ70sxB4HHga+A2IxVXloqDCYdXuqTFjV0qp5iCun5tKKaVU/YnIfwGbMebS5h6LUkp5i+YgK6WU8oiItMFVvm4xrgV9VwIT3P8qpVSroTPISimlPCIiAcDnuDYaCQB2AM+4dxFUSqlWQwNkpZRSSimlKtBFekoppZRSSlWgAbJSSimllFIVaICslFJKKaVUBRogK6WUUkopVYEGyEoppZRSSlXw/4ul+W2aBvEnAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fe43b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(0, 8, 500).reshape(-1, 1),\n",
    "        np.linspace(0, 3.5, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "\n",
    "y_proba = softmax_reg.predict_proba(X_new)\n",
    "y_predict = softmax_reg.predict(X_new)\n",
    "\n",
    "zz1 = y_proba[:, 1].reshape(x0.shape)\n",
    "zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==2, 0], X[y==2, 1], \"g^\", label=\"Iris-Virginica\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"bs\", label=\"Iris-Versicolor\")\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"yo\", label=\"Iris-Setosa\")\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "\n",
    "plt.contourf(x0, x1, zz, cmap=custom_cmap)\n",
    "contour = plt.contour(x0, x1, zz1, cmap=plt.cm.brg)\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.legend(loc=\"center left\", fontsize=14)\n",
    "plt.axis([0, 7, 0, 3.5])\n",
    "save_fig(\"softmax_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict([[5, 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6.33134077e-07, 5.75276067e-02, 9.42471760e-01]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict_proba([[5, 2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. to 11."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See appendix A."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12. Batch Gradient Descent with early stopping for Softmax Regression\n",
    "(without using Scikit-Learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start by loading the data. We will just reuse the Iris dataset we loaded earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = iris[\"target\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to add the bias term for every instance ($x_0 = 1$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_with_bias = np.c_[np.ones([len(X), 1]), X]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And let's set the random seed so the output of this exercise solution is reproducible:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(2042)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The easiest option to split the dataset into a training set, a validation set and a test set would be to use Scikit-Learn's `train_test_split()` function, but the point of this exercise is to try understand the algorithms by implementing them manually. So here is one possible implementation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_ratio = 0.2\n",
    "validation_ratio = 0.2\n",
    "total_size = len(X_with_bias)\n",
    "\n",
    "test_size = int(total_size * test_ratio)\n",
    "validation_size = int(total_size * validation_ratio)\n",
    "train_size = total_size - test_size - validation_size\n",
    "\n",
    "rnd_indices = np.random.permutation(total_size)\n",
    "\n",
    "X_train = X_with_bias[rnd_indices[:train_size]]\n",
    "y_train = y[rnd_indices[:train_size]]\n",
    "X_valid = X_with_bias[rnd_indices[train_size:-test_size]]\n",
    "y_valid = y[rnd_indices[train_size:-test_size]]\n",
    "X_test = X_with_bias[rnd_indices[-test_size:]]\n",
    "y_test = y[rnd_indices[-test_size:]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The targets are currently class indices (0, 1 or 2), but we need target class probabilities to train the Softmax Regression model. Each instance will have target class probabilities equal to 0.0 for all classes except for the target class which will have a probability of 1.0 (in other words, the vector of class probabilities for ay given instance is a one-hot vector). Let's write a small function to convert the vector of class indices into a matrix containing a one-hot vector for each instance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "def to_one_hot(y):\n",
    "    n_classes = y.max() + 1\n",
    "    m = len(y)\n",
    "    Y_one_hot = np.zeros((m, n_classes))\n",
    "    Y_one_hot[np.arange(m), y] = 1\n",
    "    return Y_one_hot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's test this function on the first 10 instances:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 1, 1, 0, 1, 1, 1, 0])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [1., 0., 0.]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "to_one_hot(y_train[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks good, so let's create the target class probabilities matrix for the training set and the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_train_one_hot = to_one_hot(y_train)\n",
    "Y_valid_one_hot = to_one_hot(y_valid)\n",
    "Y_test_one_hot = to_one_hot(y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's implement the Softmax function. Recall that it is defined by the following equation:\n",
    "\n",
    "$\\sigma\\left(\\mathbf{s}(\\mathbf{x})\\right)_k = \\dfrac{\\exp\\left(s_k(\\mathbf{x})\\right)}{\\sum\\limits_{j=1}^{K}{\\exp\\left(s_j(\\mathbf{x})\\right)}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "def softmax(logits):\n",
    "    exps = np.exp(logits)\n",
    "    exp_sums = np.sum(exps, axis=1, keepdims=True)\n",
    "    return exps / exp_sums"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are almost ready to start training. Let's define the number of inputs and outputs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_inputs = X_train.shape[1] # == 3 (2 features plus the bias term)\n",
    "n_outputs = len(np.unique(y_train))   # == 3 (3 iris classes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now here comes the hardest part: training! Theoretically, it's simple: it's just a matter of translating the math equations into Python code. But in practice, it can be quite tricky: in particular, it's easy to mix up the order of the terms, or the indices. You can even end up with code that looks like it's working but is actually not computing exactly the right thing. When unsure, you should write down the shape of each term in the equation and make sure the corresponding terms in your code match closely. It can also help to evaluate each term independently and print them out. The good news it that you won't have to do this everyday, since all this is well implemented by Scikit-Learn, but it will help you understand what's going on under the hood.\n",
    "\n",
    "So the equations we will need are the cost function:\n",
    "\n",
    "$J(\\mathbf{\\Theta}) =\n",
    "- \\dfrac{1}{m}\\sum\\limits_{i=1}^{m}\\sum\\limits_{k=1}^{K}{y_k^{(i)}\\log\\left(\\hat{p}_k^{(i)}\\right)}$\n",
    "\n",
    "And the equation for the gradients:\n",
    "\n",
    "$\\nabla_{\\mathbf{\\theta}^{(k)}} \\, J(\\mathbf{\\Theta}) = \\dfrac{1}{m} \\sum\\limits_{i=1}^{m}{ \\left ( \\hat{p}^{(i)}_k - y_k^{(i)} \\right ) \\mathbf{x}^{(i)}}$\n",
    "\n",
    "Note that $\\log\\left(\\hat{p}_k^{(i)}\\right)$ may not be computable if $\\hat{p}_k^{(i)} = 0$. So we will add a tiny value $\\epsilon$ to $\\log\\left(\\hat{p}_k^{(i)}\\right)$ to avoid getting `nan` values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 5.446183864821945\n",
      "500 0.8351003035768683\n",
      "1000 0.6876961554414912\n",
      "1500 0.6010299835452122\n",
      "2000 0.5442782811959167\n",
      "2500 0.5037262742244605\n",
      "3000 0.4728357293908468\n",
      "3500 0.4481872508179334\n",
      "4000 0.4278347262806174\n",
      "4500 0.4105891022823527\n",
      "5000 0.39568032574889406\n"
     ]
    }
   ],
   "source": [
    "eta = 0.01\n",
    "n_iterations = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-7\n",
    "\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    logits = X_train.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    if iteration % 500 == 0:\n",
    "        print(iteration, loss)\n",
    "    gradients = 1/m * X_train.T.dot(error)\n",
    "    Theta = Theta - eta * gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And that's it! The Softmax model is trained. Let's look at the model parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.3172417 , -0.6476445 , -2.99855999],\n",
       "       [-1.16505434,  0.11283387,  0.10251113],\n",
       "       [-0.72087779, -0.083875  ,  1.48587045]])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make predictions for the validation set and check the accuracy score:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9666666666666667"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_valid)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, this model looks pretty good. For the sake of the exercise, let's add a bit of $\\ell_2$ regularization. The following training code is similar to the one above, but the loss now has an additional $\\ell_2$ penalty, and the gradients have the proper additional term (note that we don't regularize the first element of `Theta` since this corresponds to the bias term). Also, let's try increasing the learning rate `eta`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 6.629574947908294\n",
      "500 0.5341631554372782\n",
      "1000 0.5037712748637474\n",
      "1500 0.4948056455575166\n",
      "2000 0.49140819484111964\n",
      "2500 0.4900085074445459\n",
      "3000 0.48940742896132616\n",
      "3500 0.4891431024691195\n",
      "4000 0.48902516549065855\n",
      "4500 0.48897205809605315\n",
      "5000 0.4889480004791563\n"
     ]
    }
   ],
   "source": [
    "eta = 0.1\n",
    "n_iterations = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-7\n",
    "alpha = 0.1  # regularization hyperparameter\n",
    "\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    logits = X_train.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    xentropy_loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n",
    "    loss = xentropy_loss + alpha * l2_loss\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    if iteration % 500 == 0:\n",
    "        print(iteration, loss)\n",
    "    gradients = 1/m * X_train.T.dot(error) + np.r_[np.zeros([1, n_outputs]), alpha * Theta[1:]]\n",
    "    Theta = Theta - eta * gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because of the additional $\\ell_2$ penalty, the loss seems greater than earlier, but perhaps this model will perform better? Let's find out:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_valid)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cool, perfect accuracy! We probably just got lucky with this validation set, but still, it's pleasant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's add early stopping. For this we just need to measure the loss on the validation set at every iteration and stop when the error starts growing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 4.70940845273367\n",
      "500 0.5740996073458012\n",
      "1000 0.5436382813658034\n",
      "1500 0.535638768431427\n",
      "2000 0.5332563789170385\n",
      "2500 0.5326544271776569\n",
      "2765 0.5326058224570446\n",
      "2766 0.5326058230506047 early stopping!\n"
     ]
    }
   ],
   "source": [
    "eta = 0.1 \n",
    "n_iterations = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-7\n",
    "alpha = 0.1  # regularization hyperparameter\n",
    "best_loss = np.infty\n",
    "\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    logits = X_train.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    xentropy_loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n",
    "    loss = xentropy_loss + alpha * l2_loss\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    gradients = 1/m * X_train.T.dot(error) + np.r_[np.zeros([1, n_outputs]), alpha * Theta[1:]]\n",
    "    Theta = Theta - eta * gradients\n",
    "\n",
    "    logits = X_valid.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    xentropy_loss = -np.mean(np.sum(Y_valid_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n",
    "    loss = xentropy_loss + alpha * l2_loss\n",
    "    if iteration % 500 == 0:\n",
    "        print(iteration, loss)\n",
    "    if loss < best_loss:\n",
    "        best_loss = loss\n",
    "    else:\n",
    "        print(iteration - 1, best_loss)\n",
    "        print(iteration, loss, \"early stopping!\")\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_valid)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Still perfect, but faster."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's plot the model's predictions on the whole dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105f47278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(0, 8, 500).reshape(-1, 1),\n",
    "        np.linspace(0, 3.5, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "X_new_with_bias = np.c_[np.ones([len(X_new), 1]), X_new]\n",
    "\n",
    "logits = X_new_with_bias.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "zz1 = Y_proba[:, 1].reshape(x0.shape)\n",
    "zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==2, 0], X[y==2, 1], \"g^\", label=\"Iris-Virginica\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"bs\", label=\"Iris-Versicolor\")\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"yo\", label=\"Iris-Setosa\")\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "\n",
    "plt.contourf(x0, x1, zz, cmap=custom_cmap)\n",
    "contour = plt.contour(x0, x1, zz1, cmap=plt.cm.brg)\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([0, 7, 0, 3.5])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now let's measure the final model's accuracy on the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9333333333333333"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_test.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_test)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our perfect model turns out to have slight imperfections. This variability is likely due to the very small size of the dataset: depending on how you sample the training set, validation set and the test set, you can get quite different results. Try changing the random seed and running the code again a few times, you will see that the results will vary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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